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Published online by Cambridge University Press:  05 December 2011

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

Addison, John W. [Add54] On Certain Points of the Theory of Recursive Functions, Ph.D. thesis, University of Wisconsin–Madison, 1954.Google Scholar
[Add04] Tarski's theory of definability: common themes in descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic, Annals of Pure and Applied Logic, vol. 126 (2004), no. 1-3, pp. 77–92.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, no. 59, 1968, pp. 708–712.CrossRefGoogle ScholarPubMed
Andretta, Alessandro [And03] Equivalence between Wadge and Lipschitz determinacy, Annals of Pure and Applied Logic, vol. 123 (2003), no. 1–3, pp. 163–192.CrossRefGoogle Scholar
Andretta, Alessandro [And06] More on Wadge determinacy, Annals of Pure and Applied Logic, vol. 144 (2006), no. 1–3, pp. 2–32.CrossRefGoogle Scholar
Andretta, Alessandro, Hjorth, Gregory, and Neeman, Itay [AHN07] Effective cardinals of boldface pointclasses, Journal of Mathematical Logic, vol. 7 (2007), no. 1, pp. 35–92.CrossRefGoogle Scholar
Andretta, Alessandro and Martin, Donald A. [AM03] Borel-Wadge degrees, Fundamenta Mathematicae, vol. 177 (2003), no. 2, pp. 175–192.CrossRefGoogle Scholar
Aumann, Robert J. and Shapley, Lloyd S. [AS74] Values of non-atomic games, Princeton University Press, 1974.Google Scholar
Barnes, John F. [Bar65] The classification of the closed-open and the recursive sets of number theoretic functions, Ph.D. thesis, UC Berkeley, 1965.Google Scholar
Becker, Howard S. [Bec85] Aproperty equivalent to the existence of scales, Transactions of the American Mathematical Society, vol. 287 (1985), pp. 591–612.CrossRefGoogle Scholar
Becker, Howard S. and Kechris, Alexander S. [BK96] The descriptive set theory of Polish group actions, London Mathematical Society Lecture Note Series, vol. 232, Cambridge University Press, Cambridge, 1996.CrossRefGoogle Scholar
Burgess, J. and Miller, D. [BM75] Remarks on invariant descriptive set theory, Fundamenta Mathematicae, vol. 90 (1975), pp. 53–75.CrossRefGoogle Scholar
Chuang, Chen-Lian [Chu82] The propagation of scales by game quantifiers, Ph.D. thesis, UCLA, 1982.Google Scholar
Davis, Morton [Dav64] Infinite games of perfect information, Advances in game theory (Dresher, Melvin, Shapley, Lloyd S., and Tucker, Alan W., editors), Annals of Mathematical Studies, vol. 52, 1964, pp. 85–101.Google Scholar
Ditzen, Achim [Dit92] Definable equivalence relations on Polish spaces, Ph.D. thesis, California Institute of Technology, 1992.Google Scholar
Duparc, Jacques [Dup01] Wadge hierarchy and Veblen hierarchy. I. Borel sets of finite rank, The Journal of Symbolic Logic, vol. 66 (2001), no. 1, pp. 56–86.CrossRefGoogle Scholar
Duparc, Jacques [Dup03] A hierarchy of deterministic context-free ω-languages, Theoretical Computer Science, vol. 290 (2003), no. 3, pp. 1253–1300.CrossRefGoogle Scholar
Duparc, Jacques, Finkel, Olivier, and Ressayre, Jean-Pierre [DFR01] Computer science and the fine structure of Borel sets, Theoretical Computer Science, vol. 257 (2001), no. 1–2, pp. 85–105.CrossRefGoogle Scholar
Friedman, Harvey [Fri71A] Determinateness in the low projective hierarchy, Fundamenta Mathematicae, vol. 72 (1971), pp. 79–95.CrossRefGoogle Scholar
Friedman, Harvey [Fri71B] Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2 (1971), no. 3, pp. 325–357.CrossRefGoogle Scholar
Friedman, Harvey and Stanley, Lee [FS89] A Borel reducibility theory for classes of countable structures, The Journal of Symbolic Logic, vol. 54 (1989), no. 3, pp. 894–914.CrossRefGoogle Scholar
Harrington, Leo A. [Har78] Analytic determinacy and 0∑ , The Journal of Symbolic Logic, vol. 43 (1978), pp. 685–693.CrossRefGoogle Scholar
Harrington, Leo A. and Kechris, Alexander S. [HK81] On the determinacy of games on ordinals, Annals of Mathematical Logic, vol. 20 (1981), pp. 109–154.CrossRefGoogle Scholar
Harrington, Leo A., Kechris, Alexander S., and Louveau, Alain [HKL90] A Glimm–Effros dichotomy for Borel equivalence relations, Journal of the American Mathematical Society, vol. 3 (1990), pp. 902–928.CrossRefGoogle Scholar
Harrington, Leo A. and Sami, Ramez-Labib [HS79] Equivalence relations, projective and beyond, Logic Colloquium '78. Proceedings of the Colloquium held in Mons, August 24–September 1, 1978 (Boffa, Maurice, Dalen, Dirk van, and McAloon, Kenneth, editors), Studies in Logic and the Foundations of Mathematics, vol. 97, North-Holland, Amsterdam, 1979, pp. 247–264.CrossRefGoogle Scholar
Hausdorff, Felix [Hau57] Set theory, Chelsea, New York, 1957, translated by J. R. Aumann.Google Scholar
Hjorth, Gregory [Hjo95] A dichotomy for the definable universe, The Journal of Symbolic Logic, vol. 60 (1995), no. 4, pp. 1199–1207.CrossRefGoogle Scholar
Hjorth, Gregory [Hjo96] Wadge degrees, Annals of Pure and Applied Logic, vol. 77 (1996), no. 1, pp. 53–74.CrossRefGoogle Scholar
Hjorth, Gregory [Hjo98] An absoluteness principle for Borel sets, The Journal of Symbolic Logic, vol. 63 (1998), no. 2, pp. 663–693.CrossRefGoogle Scholar
Hjorth, Gregory [Hjo01] A boundedness lemma for iterations, The Journal of Symbolic Logic, vol. 66 (2001), no. 3, pp. 1058–1072.CrossRefGoogle Scholar
Hjorth, Gregory [Hjo02] Cardinalities in the projective hierarchy, The Journal of Symbolic Logic, vol. 67 (2002), no. 4, pp. 1351–1372.CrossRefGoogle Scholar
Hjorth, Gregory and Kechris, Alexander S. [HK01] Recent developments in the theory of Borel reducibility, Fundamenta Mathematicae, vol. 170 (2001), no. 1–2, pp. 21–52.CrossRefGoogle Scholar
Jackson, Stephen [Jac88] AD and the projective ordinals, this volume, originally published inKechris et al. [Cabal iv], pp. 117–220.CrossRefGoogle Scholar
Jackson, Stephen [Jac90A] A new proof of the strong partition relation on ω1 , Transactions of the American Mathematical Society, vol. 320 (1990), no. 2, pp. 737–745.Google Scholar
Jackson, Stephen [Jac90B] Partition properties and well-ordered sequences, Annals of Pure and Applied Logic, vol. 48 (1990), no. 1, pp. 81–101.CrossRefGoogle Scholar
Jackson, Stephen [Jac91] Admissible Suslin cardinals in L(ℝ), The Journal of Symbolic Logic, vol. 56 (1991), no. 1, pp. 260–275.CrossRefGoogle Scholar
Jackson, Stephen [Jac99] A computation of, vol. 140, Memoirs of the AMS, no. 670, American Mathematical Society, July 1999.CrossRefGoogle 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 [Jac11] Projective ordinals. Introduction to Part IV, 2011, this volume.Google Scholar
Jackson, Stephen and Khafizov, Farid [JK] Descriptions and cardinals below, in submission.Google Scholar
Jackson, Stephen and Löwe, Benedikt [JL] Canonical measure assignments, in submission.Google Scholar
Jech, Thomas J. [Jec71] Lectures in set theory, with particular emphasis on the method of forcing, Lecture Notes in Mathematics, Vol. 217, Springer-Verlag, Berlin, 1971.CrossRefGoogle Scholar
John, Thomas [Joh86] Recursion in Kolmogorov's R-operator and the ordinal σ3 , The Journal of Symbolic Logic, vol. 51 (1986), no. 1, pp. 1–11.CrossRefGoogle Scholar
Kanamori, Akihiro and Foreman, Matthew [KF10] Handbook of set theory, Springer, 2010.Google Scholar
Kantorovich, L. and Livenson, E. [KL32] Memoir on the analytical operations and projective sets I, Fundamenta Mathematicae, vol. 18 (1932), pp. 214–279.CrossRefGoogle Scholar
Kechris, Alexander S. [Kec73] Measure and category in effective descriptive set theory, Annals of Mathematical Logic, vol. 5 (1973), no. 4, pp. 337–384.CrossRefGoogle Scholar
Kechris, Alexander S. [Kec74] On projective ordinals, The Journal of Symbolic Logic, vol. 39 (1974), pp. 269–282.CrossRefGoogle Scholar
Kechris, Alexander S. [Kec75] The theory of countable analytical sets, Transactions of the American Mathematical Society, vol. 202 (1975), pp. 259–297.CrossRefGoogle Scholar
Kechris, Alexander S. [Kec77A] AD and infinite exponent partition relations, circulated manuscript, 1977.Google Scholar
Kechris, Alexander S. [Kec77B] Classifying projective-like hierarchies, Bulletin of the Greek Mathematical Society, vol. 18 (1977), pp. 254–275.Google Scholar
Kechris, Alexander S. [Kec78] AD and projective ordinals, this volume, originally published inKechris and Moschovakis [Cabal i], pp. 91–132.CrossRefGoogle Scholar
Kechris, Alexander S. [Kec81A] Homogeneous trees and projective scales, this volume, originally published in Kechris et al. [Cabal ii], pp. 33–74.CrossRefGoogle Scholar
Kechris, Alexander S. [Kec81B] Suslin cardinals, κ-Suslin sets, and the scale property in the hyperprojective hierarchy, in Kechris et al. [Cabal ii], pp. 127–146, reprinted in [Cabal I], p. 314–332.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 (Judah, H., Just, W., and Woodin, H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer, New York, 1992, pp. 89–102.Google Scholar
Kechris, Alexander S. [Kec94] Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer, 1994.Google Scholar
Kechris, Alexander S., Kleinberg, Eugene M., Moschovakis, Yiannis N., and Woodin, W. Hugh [KKMW81] The axiom of determinacy, strong partition properties, and nonsingular measures, in Kechris et al. [Cabal ii], pp. 75–99, reprinted in [Cabal I], p. 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.Google Scholar
Kechris, Alexander S. and Martin, Donald A. [KM78] On the theory of sets of reals, Bulletin of the American Mathematical Society, vol. 84 (1978), no. 1, pp. 149–151.CrossRefGoogle Scholar
Kechris, Alexander S., Martin, Donald A., and Moschovakis, Yiannis N. [Cabal ii] Cabal seminar 77–79, Lecture Notes in Mathematics, no. 839, Berlin, Springer, 1981.CrossRefGoogle Scholar
Kechris, Alexander S., Martin, Donald A., and Moschovakis, Yiannis N. [Cabal iii] Cabal seminar 79–81, Lecture Notes in Mathematics, no. 1019, Berlin, Springer, 1983.CrossRefGoogle Scholar
Kechris, Alexander S., Martin, Donald A., and Steel, John R. [Cabal iv] Cabal seminar 81–85, Lecture Notes in Mathematics, no. 1333, Berlin, Springer, 1988.CrossRefGoogle Scholar
Kechris, Alexander S. and Moschovakis, Yiannis N. [KM72] Two theorems about projective sets, Israel Journal of Mathematics, vol. 12 (1972), pp. 391–399.CrossRefGoogle Scholar
Kechris, Alexander S. and Moschovakis, Yiannis N. [Cabal i] Cabal seminar 76–77, Lecture Notes in Mathematics, no. 689, Berlin, Springer, 1978.CrossRefGoogle 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], p. 28–74.Google Scholar
Kechris, Alexander S., Solovay, Robert M., and Steel, John R. [KSS81] The axiom of determinacy and the prewellordering property, this volume, originally published in Kechris et al. [Cabal ii], pp. 101–125.Google Scholar
Kechris, Alexander S. and Woodin, W. Hugh [KW80] Generic codes for uncountable ordinals, partition properties, and elementary embeddings, circulated manuscript, 1980, reprinted in [Cabal I], p. 379–397.Google Scholar
Kleene, Stephen C. [Kle50] Asymmetric form ofGödel's theorem, Indagationes Mathematicae, vol. 12 (1950), pp. 244–246.Google Scholar
Kleinberg, Eugene M.[Kle70] Strong partition properties for infinite cardinals, The Journal of Symbolic Logic, vol. 35 (1970), pp. 410–428.CrossRefGoogle Scholar
Kunen, Kenneth [Kun71A] Measurability of, circulated note, April 1971.Google Scholar
Kunen, Kenneth [Kun71B] On, circulated note, August 1971.Google Scholar
Kunen, Kenneth [Kun71C] A remark on Moschovakis' uniformization theorem, circulated note, March 1971.Google Scholar
Kunen, Kenneth [Kun71D] Some singular cardinals, circulated note, September 1971.Google Scholar
Kunen, Kenneth [Kun71E] Some more singular cardinals, circulated note, September 1971.Google Scholar
Kuratowski, Casimir [Kur58] Topologie. Vol. I, 4èeme ed., Monografie Matematyczne, vol. 20, Państwowe Wydawnictwo Naukowe, Warsaw, 1958.Google Scholar
Kuratowski, Kazimierz [Kur66] Topology, vol. 1, Academic Press, New York and London, 1966.Google Scholar
Laver, Richard [Lav71] On Fraïssé's order type conjecture, Annals of Mathematics, vol. 93 (1971), pp. 89–111.CrossRefGoogle Scholar
Louveau, Alain [Lou80] A separation theorem for sets, Transactions of the American Mathematical Society, vol. 260 (1980), no. 2, pp. 363–378.Google Scholar
Louveau, Alain [Lou83] Some results in the Wadge hierarchy of Borel sets, this volume, originally published in Kechris et al. [Cabal iii], pp. 28–55.CrossRefGoogle Scholar
Louveau, Alain [Lou92] Classifying Borel structures, Set Theory of the Continuum. Papers from the workshop held in Berkeley, California, October 16–20, 1989 (Judah, H., Just, W., and Woodin, H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer, New York, 1992, pp. 103–112.Google Scholar
Louveau, Alain [Lou94] On the reducibility order between Borel equivalence relations, Logic, Methodology and Philosophy of Science, IX. Proceedings of the Ninth International Congress held in Uppsala, August 7–14, 1991 (Prawitz, Dag, Skyrms, Brian, and Westerstähl, Dag, editors), Studies in Logic and the Foundations of Mathematics, vol. 134, North-Holland, Amsterdam, 1994.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. 431–467.CrossRefGoogle Scholar
Louveau, Alain and Saint-Raymond, Jean [LSR88A] Les propriétés de réduction et de norme pour les classes de Boréliens, Fundamenta Mathematicae, vol. 131 (1988), no. 3, pp. 223–243.CrossRefGoogle Scholar
Louveau, Alain and Saint-Raymond, Jean [LSR88B] The strength of Borel Wadge determinacy, this volume, originally published in Kechris et al. [Cabal iv], pp. 1–30.CrossRefGoogle Scholar
Louveau, Alain and Saint-Raymond, Jean [LSR90] On the quasi-ordering of Borel linear orders under embeddability, The Journal of Symbolic Logic, vol. 55 (1990), no. 2, pp. 537–560.CrossRefGoogle Scholar
Luzin, Nikolai [Luz30] Leçons sur les ensembles analytiques et leurs applications, Collection de monographies sur la théorie des fonctions, Gauthier-Villars, Paris, 1930.Google Scholar
Luzin, Nikolai and Sierpiński, Waclaw [LS29] Sur les classes des constituantes d'un complémentaire analytique, Comptes rendus hebdomadaires des séances de l'Académie des Sciences, vol. 189 (1929), pp. 794–796.Google Scholar
Mansfield, Richard [Man71] A Souslin operation on, Israel Journal of Mathematics, vol. 9 (1971), no. 3, pp. 367–379.CrossRefGoogle Scholar
Mansfield, Richard and Weitkamp, Galen [MW85] Recursive aspects of descriptive set theory, Oxford Logic Guides, vol. 11, The Clarendon Press Oxford University Press, New York, 1985, With a chapter by Stephen Simpson.Google Scholar
Martin, Donald A. [Mar] AD and the normal measures on, unpublished.Google 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. 687–689.CrossRefGoogle Scholar
Martin, Donald A. [Mar70] Measurable cardinals and analytic games, Fundamenta Mathematicae, vol. 66 (1970), pp. 287–291.Google Scholar
Martin, Donald A. [Mar71A] Determinateness implies many cardinals are measurable, circulated note, May 1971.Google Scholar
Martin, Donald A. [Mar71B] Projective sets and cardinal numbers: some questions related to the continuum problem, this volume, originally a preprint, 1971.Google Scholar
Martin, Donald A. [Mar73] The Wadge degrees are wellordered, unpublished, 1973.Google Scholar
Martin, Donald A. [Mar75] Borel determinacy, Annals of Mathematics, vol. 102 (1975), no. 2, pp. 363–371.CrossRefGoogle Scholar
Martin, Donald A. [Mar77A] games, planned but unfinished paper, 1977.Google Scholar
Martin, Donald A. [Mar77B] On subsets of, circulated note, January 1977.Google 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 sets of reals, Annals of Mathematics, vol. 89 (1969), pp. 138–160.CrossRefGoogle Scholar
Martin, Donald A. and Solovay, Robert M. [MS70] Internal Cohen extensions, Annals of Mathematical Logic, vol. 2 (1970), no. 2, pp. 143–178.CrossRefGoogle Scholar
Martin, Donald A. and Steel, John R. [MS83] The extent of scales in, in Kechris et al. [Cabal iii], pp. 86–96, reprinted in [Cabal I], p. 110–120.CrossRefGoogle Scholar
Moschovakis, Yiannis N. [Mos67] Hyperanalytic predicates, Transactions of the American Mathematical Society, vol. 129 (1967), pp. 249–282.CrossRefGoogle 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 (Bar-Hillel, Y., editor), Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam-London, 1970, pp. 24–62.Google Scholar
Moschovakis, Yiannis N. [Mos71] Uniformization in a playful universe, Bulletin of the American Mathematical Society, vol. 77 (1971), pp. 731–736.CrossRefGoogle Scholar
Moschovakis, Yiannis N. [Mos74] Elementary induction on abstract structures, North-Holland, 1974.Google Scholar
Moschovakis, Yiannis N. [Mos80] Descriptive set theory, Studies in Logic and the Foundations of Mathematics, no. 100, North-Holland, Amsterdam, 1980.Google Scholar
Ros, Luca Motto [MR07] General reducibilities for sets of reals, Ph.D. thesis, Politecnico di Torino, 2007.Google Scholar
Mycielski, Jan [Myc64] On the axiom of determinateness, Fundamenta Mathematicae, vol. 53 (1964), pp. 205–224.CrossRefGoogle 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. 1–3.Google Scholar
Oxtoby, John C. [Oxt71] Measure and category, Springer, 1971.CrossRefGoogle Scholar
Robertson, Neil and Seymour, P. D. [RS04] Graph minors. XX. Wagner's conjecture, Journal of Combinatorial Theory. Series B, vol. 92 (2004), no. 2, pp. 325–357.CrossRefGoogle Scholar
Rogers, Hartley [Rog59] Computing degrees of unsolvability, Mathematische Annalen, vol. 138 (1959), pp. 125–140.CrossRefGoogle Scholar
Saint-Raymond, Jean [SR76] Fonctions boréliennes sur un quotient, Bulletin des Sciences Mathématiques, vol. 100 (1976), pp. 141–147.Google Scholar
Shoenfield, Joseph R. [Sho61] The problem of predicativity, Essays on the foundations of mathematics (E. I., Yehoshua Bar-Hillel , J. Poznanski, Rabin, Michael O., and Robinson, Abraham, editors), Magnes Press, Jerusalem, 1961, pp. 132–139.Google Scholar
Shoenfield, Joseph R. [Sho67] Mathematical logic, Addison-Wesley, 1967.Google Scholar
Sierpiński, Waclaw [Sie52] General topology, Mathematical Expositions, No. 7, University of Toronto Press, Toronto, 1952, Translated by Krieger, C. Cecilia.CrossRefGoogle Scholar
Sikorski, Roman [Sik58] Some examples of Borel sets, Colloquium Mathematicum, vol. 5 (1958), pp. 170–171.CrossRefGoogle Scholar
Silver, Jack [Sil80] Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Annals of Mathematical Logic, vol. 18 (1980), no. 1, pp. 1–28.CrossRefGoogle Scholar
Simms, John [Sim79] Semihypermeasurables and games, Ph.D. thesis, Rockefeller University, 1979.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 set of integers, Transactions of the American Mathematical Society, vol. 127 (1967), no. 1, pp. 50–75.Google Scholar
Solovay, Robert M. [Sol78A] A coding of the subsets of ωω , this volume, originally published in Kechris and Moschovakis [Cabal i], pp. 133–150.CrossRefGoogle Scholar
Solovay, Robert M. [Sol78B] The independence of DC from AD, in Kechris and Moschovakis [Cabal i], pp. 171–184.CrossRefGoogle Scholar
Steel, John R. [Ste77] Determinateness and subsystems of analysis, Ph.D. thesis, Berkeley, 1977.Google Scholar
Steel, John R. [Ste80] Analytic sets and Borel isomorphisms, Fundamenta Mathematicae, vol. 108 (1980), no. 2, pp. 83–88.CrossRefGoogle Scholar
Steel, John R. [Ste81A] Closure properties of pointclasses, this volume, originally published in Kechris et al. [Cabal ii], pp. 147–163.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. [Ste82] A classification of jump operators, The Journal of Symbolic Logic, vol. 47 (1982), no. 2, pp. 347–358.CrossRefGoogle Scholar
Steel, John R. [Ste83] Scales in L(ℝ), in Kechris et al. [Cabal iii], pp. 107–156, reprinted in [Cabal I], p. 130–175.CrossRefGoogle Scholar
Steel, John R. [Ste95] HODL(ℝ) is a core model below Θ, The Bulletin of Symbolic Logic, vol. 1 (1995), pp. 75–84.CrossRefGoogle Scholar
Steel, John R. and Wesep, Robert Van [SVW82] Two consequences of determinacy consistent with choice, Transactions of the American Mathematical Society, (1982), no. 272, pp. 67–85.CrossRefGoogle 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. 88–91.Google Scholar
Tarski, Alfred [Tar00] Address at the Princeton University Bicentennial Conference on Problems of Mathematics (December 17–19, 1946), The Bulletin of Symbolic Logic, vol. 6 (2000), no. 1, pp. 1–44.Google Scholar
Engelen, Fons van, Miller, Arnold W., and Steel, John R. [vEMS87] Rigid Borel sets and better quasi-order theory, Proceedings of the AMS-IMS-SIAM joint summer research conference on applications of mathematical logic to finite combinatorics held at Humboldt State University, Arcata, Calif., August 4–10, 1985, (Simpson, Stephen G., editor), Contemporary Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1987, pp. 199–222.Google Scholar
Wesep, Robert Van [Van77] Subsystems of second-order arithmetric, and descriptive set theory under the axiom of determinateness, Ph.D. thesis, University of California, Berkeley, 1977.Google Scholar
Wesep, Robert Van [Van78A] Separation principles and the axiom of determinateness, The Journal of Symbolic Logic, vol. 43 (1978), no. 1, pp. 77–81.CrossRefGoogle Scholar
Wesep, Robert Van [Van78B] Wadge degrees and descriptive set theory, this volume, originally published in Kechris and Moschovakis [Cabal i], pp. 151–170.Google Scholar
Veblen, Oswald [Veb08] Continuous increasing functions of finite and transfinite ordinals, Transactions of the American Mathematical Society, vol. 9 (1908), no. 3, pp. 280–292.CrossRefGoogle Scholar
Wadge, William W. [Wad84] Reducibility and determinateness on the Baire space, Ph.D. thesis, University of California, Berkeley, 1984.Google Scholar
Wadge, William W. [Wad11] Early investigations of the degrees of Borel sets, 2011, this volume.Google Scholar
Woodin, W. Hugh [Woo99] The axiom of determinacy, forcing axioms, and the nonstationary ideal, De Gruyter Series in Logic and its Applications, Walter de Gruyter, Berlin, 1999.CrossRefGoogle Scholar
Zermelo, Ernst [Zer13] Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of the Fifth International Congress of Mathematicians (Hobson, E. W. and Love, A. E. H., editors), vol. 2, 1913, pp. 501–504.Google Scholar

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