Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-qdp55 Total loading time: 0.7 Render date: 2021-12-02T14:13:54.381Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Bibliography

Published online by Cambridge University Press:  27 October 2020

Alexander S. Kechris
Affiliation:
California Institute of Technology
Benedikt Löwe
Affiliation:
Universiteit van Amsterdam
John R. Steel
Affiliation:
University of California, Berkeley
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Large Cardinals, Determinacy and Other Topics
The Cabal Seminar, Volume IV
, pp. 281 - 300
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

ADDISON, JOHN W. [Add58A] Separation principles in the hierarchies of classical and effective descriptive set theory, Fundamenta Mathematicae, vol. 46 (1958–9), pp. 123135.CrossRefGoogle Scholar
ADDISON, JOHN W. AND MOSCHOVAKIS, YIANNIS N. [Add58B] Some consequences of the axiom of constructibility, Fundamenta Mathematicae, vol. 46 (1958–9), pp. 337357.CrossRefGoogle Scholar
ADDISON, JOHN W. AND MOSCHOVAKIS, YIANNIS N. [AM68] Some consequences of the axiom of definable determinateness, Proceedings of the National Academy of Sciences of the United States of America, vol. 59 (1968), pp. 708712.CrossRefGoogle Scholar
ALBERS, DONALD J. AND ALEXANDERSON, GERALD L. [AA85] Mathematical People. Profiles and Interviews, Birkhäuser, Boston, MA, 1985.Google Scholar
ANDRETTA, ALESSANDRO, NEEMAN, ITAY, AND STEEL, JOHN R. [ANS01] The domestic levels of Kc are iterable, Israel Journal of Mathematics, vol. 125 (2001), pp. 157201.CrossRefGoogle Scholar
APTER, ARTHUR W., JACKSON, STEPHEN C., AND LÖWE, BENEDIKT [AJL13] Cofinality and measurability of the first three uncountable cardinals, Transactions of the American Mathematical Society, vol. 365 (2013), no. 1, pp. 5998.CrossRefGoogle Scholar
ATMAI, RACHID [Atm19] An analysis of the models L[T2n], The Journal of Symbolic Logic, vol. 84 (2019), pp. 126.CrossRefGoogle Scholar
ATMAI, RACHID AND SARGSYAN, GRIGOR [AS19] HOD up to ADR + Θ is measurable, Annals of Pure and Applied Logic, vol. 170 (2019), no. 1, pp. 95108.CrossRefGoogle Scholar
BAGARIA, JOAN, CASTELLS, NEUS, AND LARSON, PAUL B. [BCL06] An Ω-logic primer, Set theory (Joan Bagaria and Stevo Todorčević, editors), Trends in Mathematics, Birkhäuser, Basel, 2006, pp. 128.Google Scholar
BAGARIA, JOAN, KOELLNER, PETER, AND WOODIN, W. HUGH [BKW17] Large cardinals beyond choice, 2017, preprint.Google Scholar
BANACH, STEFAN AND TARSKI, ALFRED [BT24] Sur la décomposition des ensembles de points en parties respectivement congruentes, Fundamenta Mathematicae, vol. 6 (1924), pp. 244277.CrossRefGoogle Scholar
BARWISE, JON [Bar76] Admissible Sets and Structures. An approach to definability theory, Perspectives in Mathematical Logic, Springer-Verlag, 1976.Google Scholar
BAUMGARTNER, JAMES E. [Bau83] Iterated forcing, Surveys in set theory (A. R. D. Mathias, editor), London Mathematical Society Lecture Note Series, vol. 87, Cambridge University Press, 1983, pp. 159.Google Scholar
BAUMGARTNER, JAMES E., MARTIN, DONALD A., AND SHELAH, SAHARON [BMS84] Axiomatic Set Theory. Proceedings of the AMS-IMS-SIAM joint summer research conference held in Boulder, Colo., June 19–25, 1983, Contemporary Mathematics, vol. 31, American Mathematical Society, 1984.Google Scholar
BECKER, HOWARD S. [Bec78] Partially playful universes, in Kechris and Moschovakis [CABAL i], pp. 55–90, reprinted in [CABAL III], pp. 49–85.CrossRefGoogle Scholar
BECKER, HOWARD S. [Bec80] Thin collections of sets of projective ordinals and analogs of L, Annals of Mathematical Logic, vol. 19 (1980), pp. 205241.CrossRefGoogle Scholar
BECKER, HOWARD S. [Bec81] AD and the supercompactness of ℵ1 , The Journal of Symbolic Logic, vol. 46 (1981), pp. 822841.CrossRefGoogle Scholar
BECKER, HOWARD S. [Bec85] A property equivalent to the existence of scales, Transactions of the American Mathematical Society, vol. 287 (1985), no. 2, pp. 591612.CrossRefGoogle Scholar
BECKER, HOWARD S. [Bec86] Inner model operators and the continuum hypothesis, Proceedings of the American Mathematical Society, vol. 96 (1986), no. 1, pp. 126129.CrossRefGoogle Scholar
BECKER, HOWARD S. AND KECHRIS, ALEXANDER S. [BK84] Sets of ordinals constructible from trees and the third Victoria Delfino problem, in Baumgartner et al. [BMS84], pp. 1329.CrossRefGoogle Scholar
BECKER, HOWARD S. AND MOSCHOVAKIS, YIANNIS N. [BM81] Measurable cardinals in playful models, in Kechris et al. [CABAL ii], pp. 203–214, reprinted in [CABAL III], pp. 115125.CrossRefGoogle Scholar
BEKKALI, MOHAMED [Bek91] Topics in Set Theory: Lebesgue measurability, large cardinals, forcing axioms, rho-functions. Notes on lectures by Stevo Todorčević, Lecture Notes in Mathematics, vol. 1476, Springer-Verlag, Berlin, 1991.CrossRefGoogle Scholar
BLACKWELL, DAVID [Bla67] Infinite games and analytic sets, Proceedings of the National Academy of Sciences of the United States of America, vol. 58 (1967), pp. 1836–1837.Google Scholar
BLACKWELL, DAVID [Bla69] Infinite Gδ -games with imperfect information, Polska Akademia Nauk. Instytut Matematyczny. Zastosowania Matematyki, vol. 10 (1969), pp. 99101.Google Scholar
BLASS, ANDREAS [Bla75] Equivalence of two strong forms of determinacy, Proceedings of the American Mathematical Society, vol. 52 (1975), pp. 373376.CrossRefGoogle Scholar
BOLD, STEFAN [Bol09] Cardinals as Ultrapowers. A Canonical Measure Analysis under the Axiom of Determinacy, Ph.D. thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, 2009.Google Scholar
BOLD, STEFAN AND LÖWE, BENEDIKT [BL07] A simple inductive measure analysis for cardinals under the Axiom of Determinacy, Advances in logic. Papers from the North Texas Logic Conference held at the University of North Texas, Denton, TX, October 8–10, 2004 (Su Gao, Steve Jackson, and Yi Zhang, editors), Contemporary Mathematics, vol. 425, American Mathematical Society, Providence, RI, 2007, pp. 2341.Google Scholar
BOURBAKI, NICOLAS [Bou75] Eléments de mathématique. Topologie générale, 3ème ed., Hermann, Paris, 1975.Google Scholar
BROUWER, L. E. J. [Bro24] Beweis dass jede volle Funktion gleichmässig stetig ist, Koninklijke Akademie van Weten-schappen te Amsterdam. Proceedings of the Section of Sciences, vol. 27 (1924), pp. 189193.Google Scholar
BURGESS, JOHN P. [Bur74] Infinitary Languages and Descriptive Set Theory, Ph.D. thesis, University of California at Berkeley, 1974.Google Scholar
BURGESS, JOHN P. [Bur78] Equivalences generated by families of Borel sets, Proceedings of the American Mathematical Society, vol. 69 (1978), no. 2, pp. 323326.CrossRefGoogle Scholar
BUSCH, DOUGLAS R. [Bus73] Some Problems Connected with the Axiom of Determinacy, Ph.D. thesis, Rockefeller University, 1973.Google Scholar
BUSCHE, DANIEL AND SCHINDLER, RALF [BS09] The strength of choiceless patterns of singular and weakly compact cardinals, Annals of Pure and Applied Logic, vol. 159 (2009), no. 1-2, pp. 198248.CrossRefGoogle Scholar
EDUARDO CAICEDO, ANDRÉS AND KETCHERSID, RICHARD [CK11] A trichotomy theorem in natural models of AD+ , Set theory and its applications. Papers from the Annual Boise Extravaganzas (BEST) held in Boise, ID, 1995–2010 (Liljana Babinkostova, Andrés E. Caicedo, Stefan Geschke, and Marion Scheepers, editors), Contemporary Mathematics, vol. 533, American Mathematical Society, 2011, pp. 227258.Google Scholar
CAICEDO, ANDRÉS EDUARDO, LARSON, PAUL B., SARGSYAN, GRIGOR, SCHINDLER, RALF, STEEL, JOHN R., AND ZEMAN, MARTIN [CLS17] Square principles in Pmax extensions, Israel Journal of Mathematics, vol. 217 (2017), no. 1, pp. 231261.CrossRefGoogle Scholar
CHOQUET, GUSTAVE [Cho55] Theory of capacities, Annales de l’Institut Fourier, vol. 5 (1955), pp. 131295.CrossRefGoogle Scholar
CHOQUET, GUSTAVE [Cho59] Forme abstraite du théorème de capacitabilité, Annales de l’Institut Fourier, vol. 9 (1959), pp. 8389.CrossRefGoogle Scholar
COOPER, S. BARRY [Coo04] Computability Theory, Chapman & Hall/CRC, Boca Raton, FL, 2004.Google Scholar
CRAWSHAW, MARK [Cra85] Explicit Formulas for the Jump of Q-Degrees, Ph.D. thesis, California Institute of Technology, 1985.Google Scholar
CUMMINGS, JAMES AND FOREMAN, MATTHEW [CF98] The tree property, Advances in Mathematics, vol. 133 (1998), no. 1, pp. 132.Google Scholar
DAVIES, ROY O. AND ROGERS, C. AMBROSE [DR69] The problem of subsets of finite positive measure, Bulletin of the London Mathematical Society, vol. 1 (1969), pp. 4754.CrossRefGoogle Scholar
DAVIS, MORTON [Dav64] Infinite games of perfect information, Advances in Game Theory (Melvin Dresher, Lloyd S. Shapley, and Alan W. Tucker, editors), Annals of Mathematical Studies, vol. 52, Princeton University Press, 1964, pp. 85101.Google Scholar
DELLACHERIE, CLAUDE [Del72] Ensembles analytiques, capacités, mesures de Hausdorff, Lecture Notes in Mathematics, vol. 295, Springer-Verlag, Heidelberg, 1972.CrossRefGoogle Scholar
DELLACHERIE, CLAUDE [Del80] Un cours sur les ensembles analytiques, Analytic sets (Developed from lectures given at the London Mathematical Society Instructional Conference on Analytic Sets, University College London, July 1978) (C. A. Rogers, J. E. Jayne, Claude Dellacherie, Flemming Topsøe, Jørgen Hoffmann-Jørgensen, Donald A. Martin, Alexander S. Kechris, and A. H. Stone, editors), Academic Press, 1980, pp. 183316.Google Scholar
DEVLIN, KEITH J. [Dev84] Constructibility, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1984.CrossRefGoogle Scholar
DIMONTE, VINCENZO [Dim11] Totally non-proper ordinals beyond L(Vλ+1), Archive for Mathematical Logic, vol. 50 (2011), no. 5-6, pp. 565584.CrossRefGoogle Scholar
DODD, ANTHONY [Dod82] The Core Model, London Mathematical Society Lecture Note Series, vol. 61, Cambridge University Press, 1982.CrossRefGoogle Scholar
DOEBLER, PHILIPP [Doe06] The 12th Delfino Problem and universally Baire sets of reals, Master’s thesis, Westfälische Wilhelms-Universität Münster, 2006. [Doe10] Stationary set preserving L-forcings and their applications, Ph.D. thesis, Westfälische Wilhelms-Universität Münster, 2010.Google Scholar
DOEBLER, PHILIPP AND SCHINDLER, RALF [DS13] The extender algebra and vagaries of Σ21 absoluteness, Münster Journal of Mathematics, vol. 6 (2013), pp. 117166.Google Scholar
DOUGHERTY, RANDALL AND KECHRIS, ALEXANDER S. [DK00] How many Turing degrees are there?, Computability Theory and its Applications. Current Trends and Open Problems. Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Colorado, Boulder, CO, June 13–17, 1999 (Peter A. Cholak, Steffen Lempp, Manuel Lerman, and Richard A. Shore, editors), Contemporary Mathematics, vol. 257, American Mathematical Society, 2000, pp. 8394.Google Scholar
DUBOSE, DERRICK ALBERT [DuB90] The equivalence of determinacy and iterated sharps, The Journal of Symbolic Logic, vol. 55 (1990), no. 2, pp. 502525.CrossRefGoogle Scholar
ERDŐS, PAUL AND HAJNAL, ANDRÁS [EH58] On the structure of set mappings, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 9 (1958), pp. 111131.CrossRefGoogle Scholar
ERDŐS, PAUL AND HAJNAL, ANDRÁS [EH66] On a problem of B. Jónsson, Bulletin de l’Académie Polonaise des Sciences, vol. 14 (1966), pp. 1923.Google Scholar
FARAH, ILIJAS [Far07] A proof of the Σ1-absoluteness2 theorem, Advances in logic. Papers from the North Texas Logic Conference held at the University of North Texas, Denton, TX, October 8–10, 2004 (Yi Zhang Su Gao, Steve Jackson, editor), Contemporary Mathematics, vol. 425, American Mathematical Society, 2007, pp. 922.Google Scholar
FARAH, ILIJAS, KETCHERSID, RICHARD O., LARSON, PAUL B., AND MAGIDOR, MENACHEM [FKLM08] Absoluteness for universally Baire sets and the uncountable II, Computational Prospects of Infinity. Part II. Presented Talks (Chitat Chong, Qi Feng, Theodore A. Slaman, W. Hugh Woodin, and Yue Yang, editors), World Scientific, 2008, pp. 163192.Google Scholar
FEFERMAN, SOLOMAN AND LÉVY, AZRIEL [FL63] Independence results in set theory by Cohen’s method II, Notices of the American Mathematical Society, vol. 10 (1963), p. 593.Google Scholar
FENG, QI, MAGIDOR, MENACHEM, AND WOODIN, W. HUGH [FMW92] Universally Baire sets of reals, in Judah et al. [JJW92], pp. 203–242.CrossRefGoogle Scholar
FOREMAN, MATTHEW [For82] Large cardinals and strong model theoretic transfer properties, Transactions of the American Mathematical Society, vol. 272 (1982), no. 2, pp. 427463.CrossRefGoogle Scholar
FOREMAN, MATTHEW [For86] Potent axioms, Transactions of the American Mathematical Society, vol. 294 (1986), no. 1, pp. 128.CrossRefGoogle Scholar
FOREMAN, MATTHEW AND LAVER, RICHARD [FL88] Some downwards transfer properties for ℵ2 , Advances in Mathematics, vol. 67 (1988), no. 2, pp. 230238.CrossRefGoogle Scholar
FOREMAN, MATTHEW, MAGIDOR, MENACHEM, AND SCHINDLER, RALF-DIETER [FMS01] The consistency strength of successive cardinals with the tree property, The Journal of Symbolic Logic, vol. 66 (2001), no. 4, pp. 18371847.CrossRefGoogle Scholar
FOREMAN, MATTHEW, MAGIDOR, MENACHEM, AND SHELAH, SAHARON [FMS88] Martin’s maximum, saturated ideals and nonregular ultrafilters. I, Annals of Mathematics, vol. 127 (1988), no. 1, pp. 147.CrossRefGoogle Scholar
FOREMAN, MATTHEW AND WOODIN, W. HUGH [FW91] The generalized continuum hypothesis can fail everywhere, Annals of Mathematics, vol. 133 (1991), no. 1, pp. 135.CrossRefGoogle Scholar
FRIEDMAN, HARVEY [Fri71A] Determinateness in the low projective hierarchy, Fundamenta Mathematicae, vol. 72 (1971), no. 1, pp. 79–95. (errata insert).Google Scholar
FRIEDMAN, HARVEY [Fri71B] Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2 (1971), no. 3, pp. 325357.CrossRefGoogle Scholar
FRIEDMAN, HARVEY [Fri73] Countable models of set theories, Cambridge Summer School in Mathematical Logic (held in Cambridge, England, August 1–21, 1971) (A. R. D. Mathias and H. Rogers, editors), Lecture Notes in Mathematics, vol. 337, Springer-Verlag, 1973, pp. 539573.CrossRefGoogle Scholar
GALE, DAVID AND STEWART, FRANK M. [GS53] Infinite games with perfect information, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, 1953, pp. 245266.Google Scholar
GITIK, MOTI [Git80] All uncountable cardinals can be singular, Israel Journal of Mathematics, vol. 35 (1980), no. 1-2, pp. 6188.Google Scholar
GITIK, MOTI, SCHINDLER, RALF, AND SHELAH, SAHARON [GSS06] PCF theory and Woodin cardinals, Logic Colloquium’02. Joint proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic and the Biannual Meeting of the German Association for Mathematical Logic and the Foundations of Exact Sciences (the Colloquium Logicum) held in Münster, August 3–11, 2002 (Zoé Chatzidakis, Peter Koepke, and Wolfram Pohlers, editors), Lecture Notes in Logic, vol. 27, Association for Symbolic Logic, 2006, pp. 172205.Google Scholar
GREEN, JOHN TOWNSEND [Gre78] Determinacy and the Existence of Large Measurable Cardinals, Ph.D. thesis, University of California at Berkeley, 1978.Google Scholar
GUASPARI, DAVID [Gua73] Thin and wellordered analytical sets, Ph.D. thesis, University of Cambridge, 1973.Google Scholar
GUASPARI, DAVID AND HARRINGTON, LEO [GH76] Characterizing C3 (the largest countable Π13 set), Proceedings of the American Mathematical Society, vol. 57 (1976), no. 1, pp. 127129.Google Scholar
HADAMARD, JACQUES [Had05] Cinq letters sur la théorie des ensembles, Bulletin de la Societé mathématique de France, vol. 33 (1905), pp. 261273.Google Scholar
HAJNAL, ANDRÁS [Haj56] On a consistency theorem connected with the generalized continuum problem, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 2 (1956), pp. 131136.CrossRefGoogle Scholar
HAJNAL, ANDRÁS [Haj61] On a consistency theorem connected with the generalized continuum problem, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 12 (1961), pp. 321376.Google Scholar
HALMOS, PAUL R. [Hal50] Measure Theory, D. Van Nostrand Company, Inc., New York, 1950.CrossRefGoogle Scholar
DAVID HAMKINS, JOEL AND WOODIN, W. HUGH [HW00] Small forcing creates neither strong nor Woodin cardinals, Proceedings of the American Mathematical Society, vol. 128 (2000), no. 10, pp. 30253029.CrossRefGoogle Scholar
HARNIK, VICTOR AND MAKKAI, MICHAEL [HM77] A tree argument in infinitary model theory, Proceedings of the American Mathematical Society, vol. 67 (1977), no. 1, pp. 309314.CrossRefGoogle Scholar
HARRINGTON, LEO A. [Har78] Analytic determinacy and 0# , The Journal of Symbolic Logic, vol. 43 (1978), no. 4, pp. 685693.CrossRefGoogle Scholar
HARRINGTON, LEO A. [Har] A powerless proof of a theorem of Silver, unpublished notes, undated.Google Scholar
HARRINGTON, LEO A. AND KECHRIS, ALEXANDER S. [HK81] On the determinacy of games on ordinals, Annals of Mathematical Logic, vol. 20 (1981), pp. 109154.Google Scholar
HAUSDORFF, FELIX [Hau08] Grundzüge einer Theorie der geordneten Mengen, Mathematische Annalen, vol. 65 (1908), pp. 435505.CrossRefGoogle Scholar
HAUSDORFF, FELIX [Hau14] Bemerkung über den Inhalt von Punktmengen, Mathematische Annalen, vol. 75 (1914), pp. 428434.CrossRefGoogle Scholar
HAUSER, KAI [Hau99] Towards a fine structural representation of the Martin-Solovay tree, 1999, preprint.Google Scholar
HAUSER, KAI [Hau00] Reflections on the last Delfino problem, Logic Colloquium’98. Proceedings of the Annual European Summer Meeting of the Association of Symbolic Logic, held in Prague, Czech Republic, August 9–15, 1998 (Samuel R. Buss, Petr Hájek, and Pavel Pudlák, editors), Lecture Notes in Logic, vol. 13, Cambridge University Press, 2000, pp. 206225.Google Scholar
HAUSER, KAI AND HJORTH, GREG [HH97] Strong cardinal in the core model, Annals of Pure and Applied Logic, vol. 83 (1997), no. 2, pp. 165198.CrossRefGoogle Scholar
HAUSER, KAI AND SCHINDLER, RALF [HS00] Projective uniformization revisited, Annals of Pure and Applied Logic, vol. 103 (2000), no. 1-3, pp. 109153.CrossRefGoogle Scholar
HENLE, JAMES, MATHIAS, A. R. D., AND WOODIN, W. HUGH [HMW85] A barren extension, Methods in mathematical logic. Proceedings of the sixth Latin American symposium on mathematical logic held in Caracas, August 1–6, 1983 (Carlos A. Di Prisco, editor), Lecture Notes in Mathematics, vol. 1130, Springer-Verlag, Berlin, 1985, pp. 195207.Google Scholar
HJORTH, GREGORY [Hjo95] The size of the ordinal u2 , Journal of the London Mathematical Society, vol. 52 (1995), no. 3, pp. 417433.CrossRefGoogle Scholar
HJORTH, GREGORY [Hjo96A] Π12 Wadge degrees, Annals of Pure and Applied Logic, vol. 77 (1996), no. 1, pp. 5374.CrossRefGoogle Scholar
HJORTH, GREGORY [Hjo96B] Variations of the Martin-Solovay tree, The Journal of Symbolic Logic, vol. 61 (1996), no. 1, pp. 4051.CrossRefGoogle Scholar
HJORTH, GREGORY [Hjo97] Some applications of coarse inner model theory, The Journal of Symbolic Logic, vol. 62 (1997), no. 2, pp. 337365.CrossRefGoogle Scholar
HOWARD, PAUL AND RUBIN, JEAN E. [HR98] Consequences of the Axiom of Choice, Mathematical Surveys and Monographs, vol. 59, American Mathematical Society, 1998.CrossRefGoogle Scholar
IKEGAMI, DAISUKE AND WOODIN, W. HUGH [IW09] Real determinacy and real Blackwell determinacy, Institut Mittag-Leffler Report No. 32, 2009/2010, Fall, 2009, available online.Google Scholar
JACKSON, STEPHEN [Jac88] AD and the projective ordinals, in Kechris et al. [CABAL iv], pp. 117–220, reprinted in [CABAL II], pp. 364–483.CrossRefGoogle Scholar
JACKSON, STEPHEN [Jac89] AD and the very fine structure of L(R), Bulletin of the American Mathematical Society, vol. 21 (1989), no. 1, pp. 7781.CrossRefGoogle Scholar
JACKSON, STEPHEN [Jac91] Admissible Suslin cardinals in L(R), The Journal of Symbolic Logic, vol. 56 (1991), no. 1, pp. 260275.CrossRefGoogle Scholar
JACKSON, STEPHEN [Jac92] Admissibility and Mahloness in L(R), Set theory of the continuum. Papers from the workshop held in Berkeley, California, October 16–20, 1989 (Haim Judah, Winfried Just, and Hugh Woodin, editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer-Verlag, 1992, pp. 6374.Google Scholar
JACKSON, STEPHEN [Jac99] A Computation of δ˜15, vol. 140, Memoirs of the AMS, no. 670, American Mathematical Society, July 1999.Google Scholar
JACKSON, STEPHEN [Jac08] Suslin cardinals, partition properties, homogeneity. Introduction to Part II, in Kechris et al. [CABAL I], pp. 273–313.CrossRefGoogle Scholar
JACKSON, STEPHEN [Jac10] Structural consequences of AD, in Kanamori and Foreman [KF10], pp. 1753–1876.CrossRefGoogle Scholar
JACKSON, STEPHEN, KETCHERSID, RICHARD, SCHLUTZENBERG, FARMER, AND WOODIN, W. HUGH [JKSW14] Determinacy and Jónsson cardinals in L(R), The Journal of Symbolic Logic, vol. 79 (2014), no. 4, pp. 11841198.CrossRefGoogle Scholar
JACKSON, STEPHEN AND KHAFIZOV, FARID [JK16] Descriptions and cardinals below δ˜15, The Journal of Symbolic Logic, vol. 81 (2016), no. 4, pp. 11771224.CrossRefGoogle Scholar
JACKSON, STEVE AND LÖWE, BENEDIKT [JL13] Canonical measure assignments, The Journal of Symbolic Logic, vol. 78 (2013), no. 2, pp. 403424.CrossRefGoogle Scholar
JAYNE, JOHN E. [Jay76] Structure of analytic Hausdorff spaces, Mathematika, vol. 23 (1976), pp. 208211.Google Scholar
JECH, THOMAS [Jec03] Set Theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003, the third millennium edition, revised and expanded.Google Scholar
JENSEN, RONALD B. [Jen72] The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308; erratum, p. 443.Google Scholar
JENSEN, RONALD B. AND STEEL, JOHN R. [JS13] K without the measurable, The Journal of Symbolic Logic, vol. 78 (2013), no. 3, pp. 708734.CrossRefGoogle Scholar
JUDAH, H., JUST, W., AND HUGH WOODIN, W. [JJW92] Set Theory of the Continuum, MSRI publications, vol. 26, Springer-Verlag, 1992.CrossRefGoogle Scholar
KAFKOULIS, GEORGE [Kaf04] Coding lemmata in L(Vλ+1 ), Archive for Mathematical Logic, vol. 43 (2004), no. 2, pp. 193213.CrossRefGoogle Scholar
KALMÁR, LÁSZLÓ [Kal28] Zur Theorie der abstrakten Spiele, Acta Scientiarum Mathematicarum (Szeged), vol. 4 (1928–29), no. 1–2, pp. 6585.Google Scholar
KANAMORI, AKIHIRO [Kan94] The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1994.Google Scholar
KANAMORI, AKIHIRO [Kan95] The emergence of descriptive set theory, From Dedekind to Gödel. Essays on the Development of the Foundations of Mathematics. Proceedings of a conference held at Boston University, Boston, MA, April 5–7, 1992 (Jaakko Hintikka, editor), Synthese Library, vol. 251, Kluwer Academic Publishers, Dordrecht, 1995, pp. 241262.Google Scholar
KANAMORI, AKIHIRO [Kan03] The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings, second ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Google Scholar
KANAMORI, AKIHIRO AND FOREMAN, MATTHEW [KF10] Handbook of Set Theory, Springer-Verlag, 2010.Google Scholar
KANAMORI, AKIHIRO AND MAGIDOR, MENACHEM [KM78] The evolution of large cardinal axioms in set theory, Higher Set Theory. Proceedings, Oberwolfach, Germany, April 13–23, 1977 (Gert H. Müller and Dana S. Scott, editors), Lecture Notes in Mathematics, vol. 669, Springer-Verlag, 1978, pp. 99275.Google Scholar
KECHRIS, ALEXANDER S. [Kec74] On projective ordinals, The Journal of Symbolic Logic, vol. 39 (1974), pp. 269282.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. [Kec75] The theory of countable analytical sets, Transactions of the American Mathematical Society, vol. 202 (1975), pp. 259297.Google Scholar
KECHRIS, ALEXANDER S. [Kec78] AD and projective ordinals, in Kechris and Moschovakis [CABAL i], pp. 91–132, reprinted in [CABAL II], pp. 304–345.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. [Kec81] Homogeneous trees and projective scales, in Kechris et al. [CABAL ii], pp. 33–74, reprinted in [CABAL II], pp. 270–303.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. [Kec84] The axiom of determinacy implies dependent choices in L(R), The Journal of Symbolic Logic, vol. 49 (1984), no. 1, pp. 161173.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. [Kec88] A coding theorem for measures, in Kechris et al. [CABAL iv], pp. 103–109, reprinted in [CABAL I], pp. 398–403.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. [Kec92] The structure of Borel equivalence relations in polish spaces, Set Theory of the Continuum. Papers from the workshop held in Berkeley, California, October 16–20, 1989 (Haim Judah, Winfried Just, and Hugh Woodin, editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer-Verlag, 1992, pp. 89102.Google Scholar
KECHRIS, ALEXANDER S. [Kec95] Classical Descriptive Set Theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, 1995.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S., KLEINBERG, EUGENE M., MOSCHOVAKIS, YIANNIS N., AND WOODIN, W. H. [KKMW81] The axiom of determinacy, strong partition properties, and nonsingular measures, in Kechris et al. [CABAL ii], pp. 75–99, reprinted in [CABAL I], pp. 333–354.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S., LÖWE, BENEDIKT, AND STEEL, JOHN R. [CABAL I] Games, Scales, and Suslin cardinals: the Cabal Seminar, volume I, Lecture Notes in Logic, vol. 31, Cambridge University Press, 2008. [CABAL II] Wadge Degrees and Projective Ordinals: the Cabal Seminar, volume II, Lecture Notes in Logic, vol. 37, Cambridge University Press, 2012. [CABAL III] Ordinal Definability and Recursion Theory: the Cabal Seminar, volume III, Lecture Notes in Logic, vol. 43, Cambridge University Press, 2016.Google Scholar
KECHRIS, ALEXANDER S. AND MARTIN, DONALD A. [KM78] On the theory of Π13 sets of reals, Bulletin of the American Mathematical Society, vol. 84 (1978), no. 1, pp. 149151.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S., MARTIN, DONALD A., AND MOSCHOVAKIS, YIANNIS N. [KMM81A] Appendix: Progress report on the Victoria Delfino problems, in Cabal Seminar 77–79[CABAL ii], pp. 273–274. [CABAL ii] Cabal Seminar 77–79, Lecture Notes in Mathematics, vol. 839, Berlin, Springer-Verlag, 1981.Google Scholar
KECHRIS, ALEXANDER S., MARTIN, DONALD A., AND MOSCHOVAKIS, YIANNIS N. [KMM83A] Appendix: Progress report on the Victoria Delfino problems, in Cabal Seminar 79–81[CABAL iii], pp. 283–284. [CABAL iii] Cabal Seminar 79–81, Lecture Notes in Mathematics, vol. 1019, Berlin, Springer-Verlag, 1983.Google Scholar
KECHRIS, ALEXANDER S., MARTIN, DONALD A., AND STEEL, JOHN R. [KMS88A] Appendix: Victoria Delfino problems II, in Cabal Seminar 81–85[CABAL iv], pp. 221– 224. [CABAL iv] Cabal Seminar 81–85, Lecture Notes in Mathematics, vol. 1333, Berlin, Springer-Verlag, 1988.Google Scholar
KECHRIS, ALEXANDER S. AND MOSCHOVAKIS, YIANNIS N. [KM72] Two theorems about projective sets, Israel Journal of Mathematics, vol. 12 (1972), pp. 391– 399.Google Scholar
KECHRIS, ALEXANDER S. AND MOSCHOVAKIS, YIANNIS N. [KM78A] Appendix. The Victoria Delfino problems, in Cabal Seminar 76–77[CABAL i], pp. 279–282.Google Scholar
KECHRIS, ALEXANDER S. AND MOSCHOVAKIS, YIANNIS N. [KM78B] Notes on the theory of scales, in Cabal Seminar 76–77[CABAL i], pp. 1–53, reprinted in [CABAL I], pp. 28–74. [CABAL i] Cabal Seminar 76–77, Lecture Notes in Mathematics, vol. 689, Berlin, Springer-Verlag, 1978.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. AND SOLOVAY, ROBERT M. [KS85] On the relative consistency strength of determinacy hypotheses, Transactions of the American Mathematical Society, vol. 290 (1985), no. 1, pp. 179211.Google Scholar
KECHRIS, ALEXANDER S., SOLOVAY, ROBERT M., AND STEEL, JOHN R. [KSS81] The axiom of determinacy and the prewellordering property, in Kechris et al. [CABAL ii], pp. 101–125, reprinted in [CABAL II], pp. 118–140.CrossRefGoogle Scholar
KECHRIS, ALEXANDER S. AND WOODIN, W. HUGH [KW83] Equivalence of partition properties and determinacy, Proceedings of the National Academy of Sciences of the United States of America, vol. 80 (1983), no. 6 i., pp. 17831786.CrossRefGoogle Scholar
KEISLER, H. JEROME [Kei71] Model Theory for Infinitary Logic, Studies in Logic and the Foundations of Mathematics, vol. 62, North-Holland, 1971.Google Scholar
KETCHERSID, RICHARD O., LARSON, PAUL B., AND ZAPLETAL, JINDŘICH [KLZ10] Regular embeddings of the stationary tower and Woodin’s Σ22 maximality theorem, The Journal of Symbolic Logic, vol. 75 (2010), pp. 711727.CrossRefGoogle Scholar
KETCHERSID, RICHARD O. AND ZOBLE, STUART [KZ06] On the extender algebra being complete, Mathematical Logic Quarterly, vol. 52 (2006), no. 6, pp. 531533.Google Scholar
KIHARA, TAKAYUKI AND MONTALBÁN, ANTONIO [KM18] The uniform Martin’s conjecture for many-one degrees, Transactions of the American Mathematical Society, vol. 370 (2018), no. 12, pp. 90259044.Google Scholar
KLEENE, STEPHEN C. [Kle38] On notation for ordinal numbers, The Journal of Symbolic Logic, vol. 3 (1938), pp. 150155.CrossRefGoogle Scholar
KLEENE, STEPHEN C. [Kle43] Recursive predicates and quantifiers, Transactions of the American Mathematical Society, vol. 53 (1943), pp. 4173.CrossRefGoogle Scholar
KLEENE, STEPHEN C. [Kle55A] Arithmetical predicates and function quantifiers, Transactions of the American Mathematical Society, vol. 79 (1955), pp. 312340.CrossRefGoogle Scholar
KLEENE, STEPHEN C. [Kle55B] Hierarchies of number-theoretic predicates, Bulletin of the American Mathematical Society, vol. 61 (1955), pp. 193213.CrossRefGoogle Scholar
KLEENE, STEPHEN C. [Kle55C] On the forms of the predicates in the theory of constructive ordinals. II, American Journal of Mathematics, vol. 77 (1955), pp. 405428.Google Scholar
KLEINBERG, EUGENE M. [Kle70] Strong partition properties for infinite cardinals, The Journal of Symbolic Logic, vol. 35 (1970), pp. 410428.Google Scholar
KLEINBERG, EUGENE M. [Kle77] Infinitary Combinatorics and the Axiom of Determinateness, Lecture Notes in Mathematics, vol. 612, Springer-Verlag, 1977.CrossRefGoogle Scholar
KOELLNER, PETER [Koe] Incompatible AD+ models, preprint.Google Scholar
KOELLNER, PETER AND WOODIN, W. HUGH [KW10] Large cardinals from determinacy, in Kanamori and Foreman [KF10], pp. 1951–2119. [KW] Foundations of set theory: The search for new axioms, in preparation.CrossRefGoogle Scholar
KONDÔ, MOTOKITI [Kon38] Sur l’uniformization des complementaires analytiques et les ensembles projectifs de la seconde classe, Japanese Journal of Mathematics, vol. 15 (1938), pp. 197230.Google Scholar
KŐNIG, DÉNES [Kőn27] Über eine Schlussweise aus dem Endlichen ins Unendliche, Acta Scientiarum Mathematicarum (Szeged), vol. 3 (1927), no. 2–3, pp. 121130.Google Scholar
KUNEN, KENNETH [Kun70] Some applications of iterated ultrapowers in set theory, Annals of Mathematical Logic, vol. 1 (1970), pp. 179227.CrossRefGoogle Scholar
KUNEN, KENNETH [Kun71A] Elementary embeddings and infinitary combinatorics, The Journal of Symbolic Logic, vol. 36 (1971), pp. 407413.CrossRefGoogle Scholar
KUNEN, KENNETH [Kun71B] A remark on Moschovakis’ uniformization theorem, circulated note, March 1971.Google Scholar
KUNEN, KENNETH [Kun71C] Some singular cardinals, circulated note, September 1971.Google Scholar
KUNEN, KENNETH [Kun71D] Some more singular cardinals, circulated note, September 1971.Google Scholar
KUNEN, KENNETH [Kun78] Saturated ideals, The Journal of Symbolic Logic, vol. 43 (1978), no. 1, pp. 6576.CrossRefGoogle Scholar
KUNEN, KENNETH [Kun80] Set Theory: An Introduction to Independence Proofs, North-Holland, 1980.Google Scholar
KUNEN, KENNETH [Kun11] Set Theory, Studies in Logic: Mathematical Logic and Foundations, vol. 34, College Publications, 2011.Google Scholar
KURATOWSKI, KAZIMIERZ [Kur36] Sur les théorèmes de séparation dans las théorie des ensembles, Fundamenta Mathematicae, vol. 26 (1936), pp. 183191.Google Scholar
KURATOWSKI, KAZIMIERZ [Kur58] Topologie. Vol. I, 4ème ed., Monografie Matematyczne, vol. 20, Państwowe Wydawnictwo Naukowe, Warsaw, 1958.Google Scholar
LARSON, PAUL B. [Lar04] The Stationary Tower: Notes on a Course by W. Hugh Woodin, University Lecture Series, vol. 32, American Mathematical Society, Providence, RI, 2004.Google Scholar
LARSON, PAUL B. [Lar05] The canonical function game, Archive for Mathematical Logic, vol. 44 (2005), no. 7, pp. 817827.CrossRefGoogle Scholar
LARSON, PAUL B. [Lar11] Three days of Ω-logic, Annals of the Japan Association for Philosophy of Science, vol. 19 (2011), pp. 5786.CrossRefGoogle Scholar
LARSON, PAUL B. [Lar12] A brief history of determinacy, Sets and Extensions in the Twentieth Century (Dov M. Gabbay, Akihiro Kanamori, and John Woods, editors), Handbook of the History of Logic, vol. 6, Elsevier, 2012, pp. 457507.CrossRefGoogle Scholar
LAVER, RICHARD [Lav82A] An (ℵ2 , ℵ2, ℵ0)-saturated ideal on ω1, Logic Colloquium’80. Papers intended for the European Summer Meeting of the Association for Symbolic Logic to have been held in Prague, August 24–30, 1980 (Dirk van Dalen, D. Lascar, and T. J. Smiley, editors), Studies in Logic and the Foundations of Mathematics, vol. 108, North-Holland, 1982, pp. 173180.Google Scholar
LAVER, RICHARD [Lav82B] Saturated ideals and nonregular ultrafilters, Patras Logic Symposion (Patras, 1980), Studies in Logic and the Foundations of Mathematics, vol. 109, North-Holland, Amsterdam, 1982, pp. 297305.CrossRefGoogle Scholar
LEBESGUE, HENRI [Leb05] Sur les fonctions représentables analytiquement, Journal de Mathématiques Pures et Appliquées, vol. 1 (1905), pp. 139216.Google Scholar
LEBESGUE, HENRI [Leb18] Remarques sur les théories de le mesure et de l’intégration, Annales de l’École Normale supérieure, vol. 35 (1918), pp. 191250.Google Scholar
LÉVY, AZRIEL [Lév57] Indépendance conditionnelle de V=L et d’axiomes qui se rattachent au système de M. Gödel, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 245 (1957), pp. 15821583.Google Scholar
LÉVY, AZRIEL [Lév60] A generalization of Gödel’s notion of constructibility, The Journal of Symbolic Logic, vol. 25 (1960), pp. 147155.CrossRefGoogle Scholar
LÉVY, AZRIEL [Lév65A] Definability in axiomatic set theory. I, Logic, Methodology and Philosophy of Science. Proceedings of the 1964 International Congress (Yehoshua Bar-Hillel, editor), Studies in Logic and the Foundations of Mathematics, North-Holland, 1965, pp. 127151.Google Scholar
LÉVY, AZRIEL [Lév65B] A hierarchy of formulas in set theory, Memoirs of the American Mathematical Society, vol. 57 (1965), p. 76.Google Scholar
LÉVY, AZRIEL [Lév79] Basic Set Theory, Springer-Verlag, Berlin, 1979.CrossRefGoogle Scholar
LOUVEAU, ALAIN [Lou79] Familles séparantes pour les ensembles analytiques, Comptes Rendus de l’Académie des Sciences, vol. 288 (1979), pp. 391394.Google Scholar
LOUVEAU, ALAIN AND SAINT-RAYMOND, JEAN [LSR87] Borel classes and closed games: Wadge-type and Hurewicz-type results, Transactions of the American Mathematical Society, vol. 304 (1987), no. 2, pp. 431467.Google Scholar
LOUVEAU, ALAIN AND SAINT-RAYMOND, JEAN [LSR88] The strength of Borel Wadge determinacy, in Kechris et al. [CABAL iv], pp. 1–30, reprinted in [CABAL II], pp. 74–101.CrossRefGoogle Scholar
LÖWE, BENEDIKT [Löw02] Kleinberg sequences and partition cardinals below δ˜15, Fundamenta Mathematicae, vol. 171 (2002), no. 1, pp. 6976.Google Scholar
LUZIN, NIKOLAI [Luz25A] Les proprietes des ensembles projectifs, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 180 (1925), pp. 18171819.Google Scholar
LUZIN, NIKOLAI [Luz25B] Sur les ensembles projectifs de M. Henri Lebesgue, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 180 (1925), pp. 13181320.Google Scholar
LUZIN, NIKOLAI [Luz25C] Sur un problème de M. Emil Borel et les ensembles projectifs de M. Henri Lebesgue: les ensembles analytiques, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 164 (1925), pp. 9194.Google Scholar
LUZIN, NIKOLAI [Luz27] Sur les ensembles analytiques, Fundamenta Mathematicae, vol. 10 (1927), pp. 195.CrossRefGoogle Scholar
LUZIN, NIKOLAI [Luz30A] Analogies entre les ensembles mesurables B et les ensembles analytiques, Fundamenta Mathematicae, vol. 16 (1930), pp. 4876.Google Scholar
LUZIN, NIKOLAI [Luz30B] Sur le problème de M. J. Hadamard d’uniformisation des ensembles, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 190 (1930), pp. 349351.Google Scholar
LUZIN, NIKOLAI AND NOVIKOV, PETR [LN35] Choix effectif d’un point dans un complemetaire analytique arbitraire, donne par un crible, Fundamenta Mathematicae, vol. 25 (1935), pp. 559560.Google Scholar
LUZIN, NIKOLAI AND SIERPIŃSKI, WAC̷LAW [LS18] Sur quelques propriétés des ensembles (A), Bulletin de l’Académie des Sciences Cracovie, Classe des Sciences Mathématiques, Série A, (1918), pp. 3548.Google Scholar
LUZIN, NIKOLAI AND SIERPIŃSKI, WAC̷LAW [LS23] Sur un ensemble non measurable B, Journal de Mathématiques Pures et Appliqueées, vol. 2 (1923), no. 9, pp. 5372.Google Scholar
MAGIDOR, MENACHEM [Mag78] On the singular cardinals problem. I, Israel Journal of Mathematics, vol. 28 (1978), no. 1–2, pp. 1–31.Google Scholar
MAGIDOR, MENACHEM [Mag80] Precipitous ideals and Σ˜14 sets, Israel Journal of Mathematics, vol. 35 (1980), no. 1-2, pp. 109134.CrossRefGoogle Scholar
MAKKAI, MICHAEL [Mak77] An “admissible” generalization of a theorem on countable Σ11 sets of reals with applications, Annals of Mathematical Logic, vol. 11 (1977), no. 1, pp. 130.Google Scholar
MANSFIELD, RICHARD [Man70] Perfect subsets of definable sets of real numbers, Pacific Journal of Mathematics, vol. 35 (1970), no. 2, pp. 451457.Google Scholar
MANSFIELD, RICHARD [Man71] A Souslin operation on Π21, Israel Journal of Mathematics, vol. 9 (1971), no. 3, pp. 367– 379.Google Scholar
MARCUS, LEO [Mar80] The number of countable models of a theory of one unary function, Fundamenta Mathematicae, vol. 108 (1980), no. 3, pp. 171181.Google Scholar
MARKS, ANDREW, SLAMAN, THEODORE A., AND STEEL, JOHN R. [MSS16] Martin’s conjecture, arithmetic equivalence, and countable Borel equivalence relations, in Kechris et al. [CABAL III], pp. 493520.CrossRefGoogle Scholar
MARTIN, DONALD A. [Mar68] The axiom of determinateness and reduction principles in the analytical hierarchy, Bulletin of the American Mathematical Society, vol. 74 (1968), pp. 687689.Google Scholar
MARTIN, DONALD A. [Mar70] Measurable cardinals and analytic games, Fundamenta Mathematicae, vol. 66 (1970), pp. 287291.Google Scholar
MARTIN, DONALD A. [Mar75] Borel determinacy, Annals of Mathematics, vol. 102 (1975), no. 2, pp. 363371.CrossRefGoogle Scholar
MARTIN, DONALD A. [Mar76] Proof of a conjecture of Friedman, Proceedings of the American Mathematical Society, vol. 55 (1976), no. 1, p. 129.Google Scholar
MARTIN, DONALD A. [Mar80] Infinite games, Proceedings of the International Congress of Mathematicatians, Helsinki 1978 (Olli Lehto, editor), Academia Scientiarum Fennica, 1980, pp. 269273.Google Scholar
MARTIN, DONALD A. [Mar83] The real game quantifier propagates scales, in Kechris et al. [CABAL iii], pp. 157–171, reprinted in [CABAL I], pp. 209–222.CrossRefGoogle Scholar
MARTIN, DONALD A. [Mar85] A purely inductive proof of Borel determinacy, Recursion Theory, Proceedings of Symposia in Pure Mathematics, vol. 42, AMS, Providence, RI, 1985, pp. 303308.Google Scholar
MARTIN, DONALD A. [Mar90] An extension of Borel determinacy, Annals of Pure and Applied Logic, vol. 49 (1990), no. 3, pp. 279293.CrossRefGoogle Scholar
MARTIN, DONALD A. [Mar98] The determinacy of Blackwell games, The Journal of Symbolic Logic, vol. 63 (1998), no. 4, pp. 15651581.CrossRefGoogle Scholar
MARTIN, DONALD A. [Mar03] A simple proof that determinacy implies Lebesgue measurability, Università e Politecnico di Torino. Seminario Matematico. Rendiconti, vol. 61 (2003), no. 4, pp. 393397.Google Scholar
MARTIN, DONALD A. [Mar20] Games of countable length, 2020, this volume. [Mar] AD and the normal measures onδ˜13, unpublished, undated.Google Scholar
MARTIN, DONALD A., MOSCHOVAKIS, YIANNIS N., AND STEEL, JOHN R. [MMS82] The extent of definable scales, Bulletin of the American Mathematical Society, vol. 6 (1982), pp. 435440.CrossRefGoogle Scholar
MARTIN, DONALD A., NEEMAN, ITAY, AND VERVOORT, MARCO [MNV03] The strength of Blackwell determinacy, The Journal of Symbolic Logic, vol. 68 (2003), no. 2, pp. 615636.CrossRefGoogle Scholar
MARTIN, DONALD A. AND PARIS, JEFF B. [MP71] AD ⇒∃ exactly 2 normal measures on ω2 , circulated note, March 1971.Google Scholar
MARTIN, DONALD A. AND SOLOVAY, ROBERT M. [MS69] A basis theorem for Σ13 sets of reals, Annals of Mathematics, vol. 89 (1969), pp. 138160.CrossRefGoogle Scholar
MARTIN, DONALD A. AND STEEL, JOHN R. [MS83] The extent of scales in L(R), in Kechris et al. [CABAL iii], pp. 86–96, reprinted in [CABAL I], pp. 110–120.CrossRefGoogle Scholar
MARTIN, DONALD A. AND STEEL, JOHN R. [MS88] Projective determinacy, Proceedings of the National Academy of Sciences of the United States of America, vol. 85 (1988), no. 18, pp. 65826586.CrossRefGoogle Scholar
MARTIN, DONALD A. AND STEEL, JOHN R. [MS89] A proof of projective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), no. 1, pp. 71125.CrossRefGoogle Scholar
MARTIN, DONALD A. AND STEEL, JOHN R. [MaS94] Iteration trees, Journal of the American Mathematical Society, vol. 7 (1994), no. 1, pp. 173.CrossRefGoogle Scholar
MARTIN, DONALD A. AND STEEL, JOHN R. [MS08] The tree of a Moschovakis scale is homogeneous, in Kechris et al. [CABAL I], pp. 404–420.CrossRefGoogle Scholar
MATHIAS, A. R. D. [Mat68] On a generalization of Ramsey’s theorem, Notices of the American Mathematical Society, vol. 15 (1968), p. 931.Google Scholar
MATHIAS, A. R. D. [Mat77] Happy families, Annals of Mathematical Logic, vol. 12 (1977), no. 1, pp. 59111.CrossRefGoogle Scholar
MAULDIN, R. DANIEL [Mau81] The Scottish Book: Mathematics from the Scottish Café, Birkhäuser, Boston, MA, 1981.Google Scholar
MILLER, ARNOLD W. [Mil77] Some Problems in Set Theory and Model Theory, Ph.D. thesis, University of California at Berkeley, 1977.Google Scholar
MILLER, ARNOLD W. [Mil95] Descriptive Set Theory and Forcing: How to prove theorems about Borel sets the hard way, Lecture Notes in Logic, vol. 4, Springer-Verlag, Berlin, 1995.CrossRefGoogle Scholar
MITCHELL, WILLIAM J. [Mit79] Hypermeasurable cardinals, Logic Colloquium’78. Proceedings of the Colloquium held in Mons, August 24–September 1, 1978 (Maurice Boffa, Dirk van Dalen, and Kenneth McAloon, editors), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam, 1979, pp. 303316.Google Scholar
MITCHELL, WILLIAM J. AND STEEL, JOHN R. [MiS94] Fine Structure and Iteration Trees, Lecture Notes in Logic, vol. 3, Springer-Verlag, Berlin, 1994.CrossRefGoogle Scholar
MOKOBODZKI, GABRIEL [Mok78] Ensembles à coupes dénombrables et capacités dominées par une mesure, Séminaire de Probabilités XII, Lecture Notes in Mathematics, vol. 649, Springer-Verlag, Heidelberg, 1978, pp. 492511.Google Scholar
MORLEY, MICHAEL [Mor70] The number of countable models, The Journal of Symbolic Logic, vol. 35 (1970), pp. 1418.CrossRefGoogle Scholar
MOSCHOVAKIS, YIANNIS N. [Mos67] Hyperanalytic predicates, Transactions of the American Mathematical Society, vol. 129 (1967), pp. 249282.CrossRefGoogle Scholar
MOSCHOVAKIS, YIANNIS N. [Mos69A] Abstract first order computability I, Transactions of the American Mathematical Society, vol. 138 (1969), pp. 427463.Google Scholar
MOSCHOVAKIS, YIANNIS N. [Mos69B] Abstract first order computability II, Transactions of the American Mathematical Society, vol. 138 (1969), pp. 464504.Google Scholar
MOSCHOVAKIS, YIANNIS N. [Mos70] Determinacy and prewellorderings of the continuum, Mathematical Logic and Foundations of Set Theory. Proceedings of an international colloquium held under the auspices of the Israel Academy of Sciences and Humanities, Jerusalem, 11–14 November 1968 (Y. Bar-Hillel, editor), Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam-London, 1970, pp. 2462.Google Scholar
MOSCHOVAKIS, YIANNIS N. [Mos71] Uniformization in a playful universe, Bulletin of the American Mathematical Society, vol. 77 (1971), pp. 731736.Google Scholar
MOSCHOVAKIS, YIANNIS N. [Mos73] Analytical definability in a playful universe, Logic, Methodology, and Philosophy of Science IV. Proceedings of the Fourth International Congress for Logic, Methodology and Philosophy of Science, Bucharest, 29 August–4 September, 1971 (Patrick Suppes, Leon Henkin, Athanase Joja, and Gr. C. Moisil, editors), North-Holland, 1973, pp. 7783.Google Scholar
MOSCHOVAKIS, YIANNIS N. [Mos78] Inductive scales on inductive sets, in Kechris and Moschovakis [CABAL i], pp. 185–192, reprinted in [CABAL I], pp. 94–101.CrossRefGoogle Scholar
MOSCHOVAKIS, YIANNIS N. [Mos80] Descriptive Set Theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland, Amsterdam, 1980.Google Scholar
MOSCHOVAKIS, YIANNIS N. [Mos81] Ordinal games and playful models, in Kechris et al. [CABAL ii], pp. 169–201, reprinted in [CABAL III], pp. 86–114.CrossRefGoogle Scholar
MOSCHOVAKIS, YIANNIS N. [Mos83] Scales on coinductive sets, in Kechris et al. [CABAL iii], pp. 77–85, reprinted in [CABAL I], pp. 102–109.CrossRefGoogle Scholar
MOSCHOVAKIS, YIANNIS N. [Mos09] Descriptive Set Theory, second ed., Mathematical Surveys and Monographs, vol. 155, American Mathematical Society, 2009.CrossRefGoogle Scholar
MÜLLER, SANDRA, SCHINDLER, RALF, AND WOODIN, W. HUGH [MSW16] Mice with finitely many Woodin cardinals from optimal determinacy hypotheses, submitted, 2016.Google Scholar
MYCIELSKI, JAN [Myc64] On the axiom of determinateness, Fundamenta Mathematicae, vol. 53 (1964), pp. 205224.Google Scholar
MYCIELSKI, JAN [Myc66] On the axiom of determinateness. II, Fundamenta Mathematicae, vol. 59 (1966), pp. 203– 212.Google Scholar
MYCIELSKI, JAN AND STEINHAUS, HUGO [MS62] A mathematical axiom contradicting the axiom of choice, Bulletin de l’Académie Polonaise des Sciences, vol. 10 (1962), pp. 13.Google Scholar
MYCIELSKI, JAN AND ŚWIERCZKOWSKI, STANIS̷LAW [MŚ64] On the Lebesgue measurability and the axiom of determinateness, Fundamenta Mathematicae, vol. 54 (1964), pp. 6771.Google Scholar
NADEL, MARK E. [Nad71] Model Theory in Admissible Sets, Ph.D. thesis, University of Wisconsin, 1971.Google Scholar
NEEMAN, ITAY [Nee95] Optimal proofs of determinacy, The Bulletin of Symbolic Logic, vol. 1 (1995), no. 3, pp. 327–339.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee00] Unraveling Π11 sets, Annals of Pure and Applied Logic, vol. 106 (2000), no. 1-3, pp. 151205.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee02A] Inner models in the region of a Woodin limit of Woodin cardinals, Annals of Pure and Applied Logic, vol. 116 (2002), no. 1-3, pp. 67155.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee02B] Optimal proofs of determinacy II, Journal of Mathematical Logic, vol. 2 (2002), no. 2, pp. 227258.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee04] The Determinacy of Long Games, de Gruyter Series in Logic and its Applications, vol. 7, Walter de Gruyter, Berlin, 2004.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee05] An introduction to proofs of determinacy of long games, Logic Colloquium’01. Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic held in Vienna, August 6–11, 2001 (Matthias Baaz, Sy-David Friedman, and Jan Krajíček, editors), Lecture Notes in Logic, vol. 20, Association for Symbolic Logic, 2005, pp. 4386.Google Scholar
NEEMAN, ITAY [Nee06A] Determinacy for games ending at the first admissible relative to the play, The Journal of Symbolic Logic, vol. 71 (2006), no. 2, pp. 425459.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee06B] Unraveling Π11 sets, revisited, Israel Journal of Mathematics, vol. 152 (2006), pp. 181203.Google Scholar
NEEMAN, ITAY [Nee07A] Games of length ω1, Journal of Mathematical Logic, vol. 7 (2007), no. 1, pp. 83124.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee07B] Inner models and ultrafilters in L(R), The Bulletin of Symbolic Logic, vol. 13 (2007), no. 1, pp. 3153.CrossRefGoogle Scholar
NEEMAN, ITAY [Nee10] Determinacy in L(R), in Kanamori and Foreman [KF10], pp. 1877–1950.CrossRefGoogle Scholar
NEEMAN, ITAY AND STEEL, JOHN R. [NS06] Counterexamples to the unique and cofinal branches hypotheses, The Journal of Symbolic Logic, vol. 71 (2006), no. 3, pp. 977988.Google Scholar
NEEMAN, ITAY AND ZAPLETAL, JINDŘICH [NZ00] Proper forcing and L(R), preprint, arXiv:0003027v1, 2000.Google Scholar
NEEMAN, ITAY AND ZAPLETAL, JINDŘICH [NZ01] Proper forcing and L(R), The Journal of Symbolic Logic, vol. 66 (2001), no. 2, pp. 801810.CrossRefGoogle Scholar
NOVIKOV, PETR [Nov35] Sur la séparabilité des ensembles projectifs de seconde class, Fundamenta Mathematicae, vol. 25 (1935), pp. 459466.Google Scholar
OXTOBY, JOHN C. [Oxt80] Measure and Category, second ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York, 1980.CrossRefGoogle Scholar
PARIS, JEFF B. [Par72] ZF ⊢ Σ04 determinateness, The Journal of Symbolic Logic, vol. 37 (1972), pp. 661667.Google Scholar
PREISS, DAVID [Pre73] Metric spaces in which Prohorov’s theorem is not valid, Zeitschrift für Wahrscheinlichkeits-theorie und Verwandte Gebiete, vol. 27 (1973), pp. 109116.CrossRefGoogle Scholar
PŘÍKRÝ, KAREL [Pří76] Determinateness and partitions, Proceedings of the American Mathematical Society, vol. 54 (1976), pp. 303306.CrossRefGoogle Scholar
RAMSEY, FRANK [Ram30] On a problem of formal logic, Proceedings of the London Mathematical Society, vol. 30 (1930), no. 2, pp. 224.Google Scholar
RUBIN, MATI [Rub74] Thoeries of linear order, Israel Journal of Mathematics, vol. 17 (1974), pp. 392443.CrossRefGoogle Scholar
RUBIN, MATI [Rub77] Vaught’s conjecture for linear orderings, Notices of the American Mathematical Society, vol. 24 (1977), p. A 390.Google Scholar
SACKS, GERALD E. [Sac76] Countable admissible ordinals and hyperdegrees, Advances in Mathematics, vol. 20 (1976), no. 2, pp. 213262.Google Scholar
SARGSYAN, GRIGOR [Sar13A] Descriptive inner model theory, The Bulletin of Symbolic Logic, vol. 19 (2013), no. 1, pp. 155.CrossRefGoogle Scholar
SARGSYAN, GRIGOR [Sar13B] On the prewellorderings associated with the directed systems of mice, The Journal of Symbolic Logic, vol. 78 (2013), no. 3, pp. 735763.Google Scholar
SARGSYAN, GRIGOR [Sar14] An inner model proof of the strong partition property for δ˜21, Notre Dame Journal of Formal Logic, vol. 55 (2014), no. 4, pp. 563568.Google Scholar
SARGSYAN, GRIGOR [Sar15] Hod Mice and the Mouse Set Conjecture, vol. 236, Memoirs of the American Mathematical Society, no. 1111, American Mathematical Society, 2015.CrossRefGoogle Scholar
SARGSYAN, GRIGOR AND TRANG, NAM [ST16] The Largest Suslin Axiom, 2016, book manuscript, submitted.Google Scholar
SCHIMMERLING, ERNEST [Sch95] Combinatorial principles in the core model for one Woodin cardinal, Annals of Pure and Applied Logic, vol. 74 (1995), no. 2, pp. 153201.Google Scholar
SCHIMMERLING, ERNEST [Sch01] The ABC’s of mice, The Bulletin of Symbolic Logic, vol. 7 (2001), no. 4, pp. 485503.CrossRefGoogle Scholar
SCHIMMERLING, ERNEST [Sch07] Coherent sequences and threads, Advances in Mathematics, vol. 216 (2007), no. 1, pp. 89– 117.Google Scholar
SCHIMMERLING, ERNEST [Sch10] A core model toolbox and guide, in Kanamori and Foreman [KF10], pp. 1685–1752. [Sch] Notes on Woodin’s extender algebra, preprint, undated.CrossRefGoogle Scholar
SCHIMMERLING, ERNEST AND ZEMAN, MARTIN [SZ01] Square in core models, The Bulletin of Symbolic Logic, vol. 7 (2001), no. 3, pp. 305314.CrossRefGoogle Scholar
SCHINDLER, RALF [Sch99] The Delfino problem # 12, Talks in Bonn, 4/ 21/ 99–4/ 23/ 99, handwritten manuscript, 50 pages, available online, 1999.Google Scholar
SCHINDLER, RALF [Sch02] The core model for almost linear iterations, Annals of Pure and Applied Logic, vol. 116 (2002), no. 1-3, pp. 205272.CrossRefGoogle Scholar
SCHWALBE, ULRICH AND WALKER, PAUL [SW01] Zermelo and the early history of game theory, Games and Economic Behavior, vol. 34 (2001), no. 1, pp. 123137.CrossRefGoogle Scholar
SHELAH, SAHARON [She84] Can you take Solovay’s inaccessible away?, Israel Journal of Mathematics, vol. 48 (1984), no. 1, pp. 147.Google Scholar
SCHINDLER, RALF [She98] Proper and Improper Forcing, second ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998.Google Scholar
SHELAH, SAHARON AND WOODIN, W. HUGH [SW90] Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable, Israel Journal of Mathematics, vol. 70 (1990), no. 3, pp. 381394.Google Scholar
SHOCHAT, DAVID DAWSON [Sho72] Capacitability of Σ˜12 sets, Ph.D. thesis, University of California at Los Angeles, 1972.Google Scholar
SHOENFIELD, JOSEPH R. [Sho61] The problem of predicativity, Essays on the Foundations of Mathematics. Dedicated to A. A. Fraenkel on his Seventieth Anniversary (Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson, editors), Magnes Press, Jerusalem, 1961, pp. 132139.Google Scholar
SHOENFIELD, JOSEPH R. [Sho67] Mathematical Logic, Addison-Wesley, 1967.Google Scholar
SIERPIŃSKI, WAC̷LAW [Sie24] Sur une propriété des ensembles ambigus, Fundamenta Mathematicae, vol. 6 (1924), pp. 15.CrossRefGoogle Scholar
SIERPIŃSKI, WAC̷LAW [Sie25] Sur une class d’ensembles, Fundamenta Mathematicae, vol. 7 (1925), pp. 237243.Google Scholar
SIERPIŃSKI, WAC̷LAW [Sie38] Fonctions additives non complètement additives et fonctions non mesurables, Fundamenta Mathematicae, vol. 30 (1938), pp. 9699.Google Scholar
SILVER, JACK H. [Sil71] Some applications of model theory in set theory, Annals of Mathematical Logic, vol. 3 (1971), no. 1, pp. 45110.Google Scholar
SILVER, JACK H. [Sil75] On the singular cardinals problem, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974), Vol. 1, Canadian Mathematical Congress, 1975, pp. 265268.Google Scholar
SILVER, JACK H. [Sil] Π˜11 equivalence relations, unpublished notes, undated.Google Scholar
SION, MAURICE [Sio63] On capacitability and measurability, Annales de l’Institut Fourier, vol. 13 (1963), pp. 8899.Google Scholar
SLAMAN, THEODORE A. [Sla09] Degree invariant functions, slides of a talk at the 2009 VIG, available online, 2009.Google Scholar
SLAMAN, THEODORE A. AND STEEL, JOHN R. [SS88] Definable functions on degrees, in Kechris et al. [CABAL iv], pp. 37–55, reprinted in [CABAL III], pp. 458–475.CrossRefGoogle Scholar
SOARE, ROBERT I. [Soa87] Recursively Enumerable Sets and Degrees, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar
SOLOVAY, ROBERT M. [Sol66] On the cardinality of Σ12 set of reals, Foundations of Mathematics: Symposium papers commemorating the 60th birthday of Kurt Gödel (Jack J. Bulloff, Thomas C. Holyoke, and S. W. Hahn, editors), Springer-Verlag, 1966, pp. 5873.Google Scholar
SOLOVAY, ROBERT M. [Sol67A] Measurable cardinals and the axiom of determinateness, lecture notes prepared in connection with the Summer Institute of Axiomatic Set Theory held at UCLA, Summer 1967.Google Scholar
SOLOVAY, ROBERT M. [Sol67B] A nonconstructible Δ13 set of integers, Transactions of the American Mathematical Society, vol. 127 (1967), no. 1, pp. 5075.Google Scholar
SOLOVAY, ROBERT M. [Sol70] A model of set-theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, vol. 92 (1970), pp. 156.Google Scholar
SOLOVAY, ROBERT M. [Sol78A] A Δ13 coding of the subsets of ωω, in Kechris and Moschovakis [CABAL i], pp. 133–150, reprinted in [CABAL II], pp. 346–363.Google Scholar
SOLOVAY, ROBERT M. [Sol78B] The independence of DC from AD, in Kechris and Moschovakis [CABAL i], pp. 171–184, reprinted in this volume.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste81A] Closure properties of pointclasses, in Kechris et al. [CABAL ii], pp. 147–163, reprinted in [CABAL II], pp. 102–117.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste81B] Determinateness and the separation property, The Journal of Symbolic Logic, vol. 46 (1981), no. 1, pp. 41–44.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste82A] A classification of jump operators, The Journal of Symbolic Logic, vol. 47 (1982), no. 2, pp. 347358.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste82B] Determinacy in the Mitchell models, Annals of Mathematical Logic, vol. 22 (1982), no. 2, pp. 109125.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste83A] Scales in L(R), in Kechris et al. [CABAL iii], pp. 107–156, reprinted in [CABAL I], pp. 130–175.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste83B] Scales on Σ11 sets, in Kechris et al. [CABAL iii], pp. 72–76, reprinted in [CABAL I], pp. 90–93.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste88] Long games, in Kechris et al. [CABAL iv], pp. 56–97, reprinted in [CABAL I], pp. 223–259.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste95A] HODL(R) is a core model below Θ, The Bulletin of Symbolic Logic, vol. 1 (1995), no. 1, pp. 7584.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste95B] Projectively wellordered inner models, Annals of Pure and Applied Logic, vol. 74 (1995), no. 1, pp. 77104.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste96] The Core Model Iterability Problem, Lecture Notes in Logic, no. 8, Springer-Verlag, Berlin, 1996.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste02] Core models with more Woodin cardinals, The Journal of Symbolic Logic, vol. 67 (2002), no. 3, pp. 11971226.Google Scholar
STEEL, JOHN R. [Ste05] PFA implies AD L(R), The Journal of Symbolic Logic, vol. 70 (2005), no. 4, pp. 12551296.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste08A] Derived models associated to mice, Computational Prospects of Infinity. Part II. Presented Talks (Chitat Chong, Qi Feng, Theodore A. Slaman, W. Hugh Woodin, and Yue Yang, editors), World Scientific, 2008, pp. 105193.Google Scholar
STEEL, JOHN R. [Ste08B] Games and scales. Introduction to Part I, in Kechris et al. [CABAL I], pp. 3–27.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste08C] The length-ω1 open game quantifier propagates scales, in Kechris et al. [CABAL I], pp. 260– 269.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste08D] Scales in K(R) at the end of a weak gap, The Journal of Symbolic Logic, vol. 73 (2008), no. 2, pp. 369390.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste08E] Scales in K(R), in Kechris et al. [CABAL I], pp. 176–208.CrossRefGoogle Scholar
STEEL, JOHN R. [Ste09] The derived model theorem, Logic Colloquium’06. Proc. of the Annual European Conference on Logic of the Association for Symbolic Logic held at the Radboud University, Nijmegen, July 27–August 2, 2006 (S. Barry Cooper, Herman Geuvers, Anand Pillay, and Jouko Väänänen, editors), Lecture Notes in Logic, vol. 19, Association for Symbolic Logic, 2009, pp. 280327.Google Scholar
STEEL, JOHN R. [Ste10] An outline of inner model theory, in Kanamori and Foreman [KF10], pp. 1595–1684.CrossRefGoogle Scholar
STEEL, JOHN R. AND TRANG, NAM [ST10] AD+ , derived models, and Σ1 reflection, Notes from the first Münster conference on the core model induction and hod mice, available online, 2010.Google Scholar
STEEL, JOHN R. AND WESEP, ROBERT VAN [SVW82] Two consequences of determinacy consistent with choice, Transactions of the American Mathematical Society, vol. 272 (1982), no. 1, pp. 6785.Google Scholar
STEEL, JOHN R. AND WOODIN, W. HUGH [SW16] HOD as a core model, in Kechris et al. [CABAL III], pp. 257–345.Google Scholar
STEEL, JOHN R. AND ZOBLE, STUART [SZ] Determinacy from strong reflection, in preparation.Google Scholar
SUSLIN, MIKHAIL YA. [Sus17] Sur une définition des ensembles mesurables B sans nombres transfinis, Comptes rendus hebdomadaires des séances de l’Académie des Sciences, vol. 164 (1917), pp. 8891.Google Scholar
TODORČEVIĆ, STEVO [Tod84] A note on the proper forcing axiom, in Baumgartner et al. [BMS84], pp. 209–218.CrossRefGoogle Scholar
TRANG, NAM [Tra14] HOD in natural models of AD+, Annals of Pure and Applied Logic, vol. 165 (2014), no. 10, pp. 15331556.CrossRefGoogle Scholar
ULAM, STANIS̷LAW [Ula60] A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, vol. 8, Interscience Publishers, New York–London, 1960.Google Scholar
WESEP, ROBERT VAN [Van78A] Separation principles and the axiom of determinateness, The Journal of Symbolic Logic, vol. 43 (1978), no. 1, pp. 7781.CrossRefGoogle Scholar
WESEP, ROBERT VAN [Van78B] Wadge degrees and descriptive set theory, in Kechris and Moschovakis [CABAL i], pp. 151–170, reprinted in [CABAL II], pp. 24–42.Google Scholar
VAUGHT, ROBERT L. [Vau74] Invariant sets in topology and logic, Fundamenta Mathematicae, vol. 82 (1974), pp. 269– 293.Google Scholar
VELIČKOVIĆ, BOBAN [Vel92] Forcing axioms and stationary sets, Advances in Mathematics, vol. 94 (1992), no. 2, pp. 256284.Google Scholar
VITALI, GIUSEPPE [Vit05] Sul problema della misura dei gruppi di punti di una retta, Tipografia Gamberini e Parmeggiani, (1905), pp. 231–235.Google Scholar
NEUMANN, JOHN VON AND MORGENSTERN, OSKAR [vNM04] Theory of Games and Economic Behavior, Princeton University Press, 2004, Reprint of the 1980 edition.Google Scholar
WAGON, STAN [Wag93] The Banach-Tarski paradox, Cambridge University Press, 1993, corrected reprint of the 1985 original.Google Scholar
WOLFE, PHILIP [Wol55] The strict determinateness of certain infinite games, Pacific Journal of Mathematics, vol. 5 (1955), pp. 841847.Google Scholar
WOODIN, W. HUGH [Woo82] On the consistency strength of projective uniformization, Proceedings of the Herbrand Symposium. Logic Colloquium’81. Held in Marseille, July 16–24, 1981 (Jacques Stern, editor), Studies in Logic and the Foundations of Mathematics, vol. 107, North-Holland, Amsterdam, 1982, pp. 365384.Google Scholar
WOODIN, W. HUGH [Woo83] Some consistency results in ZFC using AD, in Kechris et al. [CABAL iii], pp. 172–198, reprinted in this volume.CrossRefGoogle Scholar
WOODIN, W. HUGH [Woo85] Σ12-absoluteness, handwritten note, May 1985.Google Scholar
WOODIN, W. HUGH [Woo86] Aspects of determinacy, Logic, Methodology and Philosophy of Science. VII. Proceedings of the Seventh International Congress held at the University of Salzburg, Salzburg, July 11–16, 1983 (Ruth Barcan Marcus, Georg J. W. Dorn, and Paul Weingartner, editors), Studies in Logic and the Foundations of Mathematics, vol. 114, North-Holland, Amsterdam, 1986, pp. 171181.Google Scholar
WOODIN, W. HUGH [Woo88] Supercompact cardinals, sets of reals, and weakly homogeneous trees, Proceedings of the National Academy of Sciences of the United States of America, vol. 85 (1988), no. 18, pp. 65876591.Google Scholar
WOODIN, W. HUGH [Woo99] The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, de Gruyter Series in Logic and its Applications, vol. 1, Walter de Gruyter, Berlin, 1999.CrossRefGoogle Scholar
WOODIN, W. HUGH [Woo01] The Ω conjecture, Aspects of Complexity. Minicourses in Algorithmics, Complexity and Computational Algebra. Proceedings of the Workshop on Computability, Complexity, and Computational Algebra held in Kaikoura, January 7–15, 2000 (Rod Downey and Denis Hirschfeldt, editors), de Gruyter Series in Logic and its Applications, vol. 4, de Gruyter, Berlin, 2001, pp. 155169.Google Scholar
WOODIN, W. HUGH [Woo02] Beyond Σ21 absoluteness, Proceedings of the International Congress of Mathematicians, Vol. I. Plenary Lectures and Ceremonies. Held in Beijing, August 20–28, 2002 (Beijing) (Tatsien Li, editor), Higher Education Press, 2002, pp. 515524.Google Scholar
WOODIN, W. HUGH [Woo08] A tt version of the Posner-Robinson theorem, Computational Prospects of Infinity. Part II. Presented Talks (Chitat Chong, Qi Feng, Theodore A. Slaman, W. Hugh Woodin, and Yue Yang, editors), World Scientific, 2008, pp. 355392.Google Scholar
WOODIN, W. HUGH [Woo10] The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, revised ed., de Gruyter Series in Logic and its Applications, vol. 1, Walter de Gruyter, Berlin, 2010. [Woo] An ℵ1 dense ideal on ℵ1, in preparation.CrossRefGoogle Scholar
ZERMELO, ERNST [Zer04] Beweis, daß jede Menge wohlgeordnet werden kann, Mathematische Annalen, vol. 59 (1904), pp. 514516.Google Scholar
ZERMELO, ERNST [Zer13] Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of the Fifth International Congress of Mathematicians, vol. 2, 1913, pp. 501504.Google Scholar
ZHU, YIZHENG [Zhu10] The derived model theorem II, Notes on lectures given by H. Woodin at the first Münster conference on the core model induction and hod mice, available online, 2010.Google Scholar
ZHU, YIZHENG [Zhu15] Realizing an AD+ model as a derived model of a premouse, Annals of Pure and Applied Logic, vol. 166 (2015), no. 12, pp. 12751364.Google Scholar
ZHU, YIZHENG [Zhu16] Lightface mice with finitely many Woodin cardinals from optimal determinacy hypotheses, 2016, preprint, arXiv 1610.02352v1.Google Scholar
ZHU, YIZHENG [Zhu17] The higher sharp I: on M#1, 2017, preprint, arXiv:1604.00481v4.Google Scholar