Skip to main content Accessibility help
×
Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T23:19:12.183Z Has data issue: false hasContentIssue false

REFERENCES

Published online by Cambridge University Press:  05 June 2012

Katrin Tent
Affiliation:
Universität Münster, Germany
Martin Ziegler
Affiliation:
Albert-Ludwigs-Universität Freiburg, Germany
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
Publisher: Cambridge University Press
Print publication year: 2012

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

[1] James, Ax, The elementary theory of finite fields, Annals of Mathematics. Second Series, vol. 88 (1968), pp. 239–271.Google Scholar
[2] J. T., Baldwin and A. H., Lachlan, On strongly minimal sets, The Journal of Symbolic Logic, vol. 36 (1971), pp. 79–96.Google Scholar
[3] John T., Baldwin, αT is finite for ℵ1–categorical T, Transactions of the American Mathematical Society, vol. 181 (1973), pp. 37–51.Google Scholar
[4] John T., Baldwin, Fundamentals of Stability Theory, Perspectives in Mathematical Logic, Springer Verlag; Berlin, Heidelberg, New York, London, Paris, Tokyo, 1988.Google Scholar
[5] John T., Baldwin, An almost strongly minimal non-Desarguesian projective plane, Transactions of the American Mathematical Society, vol. 342 (1994), no. 2, pp. 695–711.Google Scholar
[6] A., Baudisch, A., Martin-Pizarro, and M., Ziegler, Red fields, The Journal of Symbolic Logic, vol. 72 (2007), no. 1, pp. 207–225.Google Scholar
[7] Andreas, Baudisch, A new uncountably categorical group, Transactions of the American Mathematical Society, vol. 348 (1996), no. 10, pp. 3889–3940.Google Scholar
[8] Andreas, Baudisch, Martin, Hils, Amador, Martin-Pizarro, and Frank O., Wagner, Die böse Farbe, Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Mathématiques de Jussieu, vol. 8 (2009), no. 3, pp. 415–443.Google Scholar
[9] Paul, Bernays, Axiomatic Set Theory With a historical introduction by Abraham A., Fraenkel, Dover Publications Inc., New York, 1991, Reprint of the 1968 edition.Google Scholar
[10] N., Bourbaki, XI, Algébre, Chapitre 5, Corps Commutatifs, Hermann, Paris, 1959.Google Scholar
[11] Elisabeth, Bouscaren, The group configuration – after E. Hrushovski, The Model Theory of Groups (Notre Dame, IN, 1985–1987), Notre Dame Math. Lectures, vol. 11, Univ. Notre Dame Press, Notre Dame, IN, 1989, pp. 199–209.Google Scholar
[12] Steven, Buechler, Essential Stability Theory, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1996.Google Scholar
[13] Francis, Buekenhout, An introduction to incidence geometry, Handbook of Incidence Geometry, North-Holland, Amsterdam, 1995, pp. 1–25.Google Scholar
[14] Enrique, Casanovas, Simple Theories and Hyperimaginaries, Lecture Notes in Logic, vol. 39, Cambridge University Press, 2011.Google Scholar
[15] C. C., Chang and H. J., Keisler, Model Theory, third ed., Studies in Logic and the Foundations of Mathematics, vol. 73, North-Holland Publishing Co., Amsterdam, 1990.Google Scholar
[16] Zoé, Chatzidakis, Théorie des modèles des corps finis et pseudo-fini, Unpublished Lecture Notes, 1996.Google Scholar
[17] Zoé, Chatzidakis and Ehud, Hrushovski, Model theory of difference fields, Transactions of the American Mathematical Society, vol. 351 (1999), no. 8, pp. 2997–3071.Google Scholar
[18] M. M., Erimbetov, Complete theories with 1-cardinal formulas, Akademiya Nauk SSSR. Sibirskoe Otdelenie. Institut Matematiki. Algebra i Logika, vol. 14 (1975), no. 3, pp. 245–257, 368.Google Scholar
[19] Ju. L., Eršov, Fields with a solvable theory, Doklady Akademii Nauk SSSR, vol. 174 (1967), pp. 19–20, English transl., Soviet Math. Dokl., 8:575-576, 1967.Google Scholar
[20] Ulrich, Felgner, Comparison of the axioms of local and universal choice, Polska Akademia Nauk. Fundamenta Mathematicae, vol. 71 (1971), no. 1, pp. 43–62, (errata insert).Google Scholar
[21] Steven, Givant and Paul, Halmos, Introduction to Boolean Algebras, Undergraduate Texts in Mathematics, Springer, New York, 2009.Google Scholar
[22] Victor, Harnik, On the existence of saturated models of stable theories, Proceedings of the American Mathematical Society, vol. 52 (1975), pp. 361–367.Google Scholar
[23] Deirdre, Haskell, Ehud, Hrushovski, and Dugald, Macpherson, Stable Domination and Independence in Algebraically Closed Valued Fields, Lecture Notes in Logic, vol. 30, Association for Symbolic Logic, Chicago, IL, 2008.Google Scholar
[24] Wilfrid, Hodges, Model Theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993.Google Scholar
[25] Wilfrid, Hodges, A Shorter Model Theory, Cambridge University Press, 1997.
[26] Ehud, Hrushovski, A stable ℵ0-categorical pseudoplane, Preprint, 1988.
[27] Ehud, Hrushovski, Unidimensional Theories are Superstable, Annals of Pure and Applied Logic, vol. 50 (1990), pp. 117–138.Google Scholar
[28] Ehud, Hrushovski, A new strongly minimal set, Stability in model theory, III (Trento, 1991), Annals of Pure and Applied Logic, vol. 62 (1993), no. 2, pp. 147–166.Google Scholar
[29] Ehud, Hrushovski, A non-PAC field whose maximal purely inseparable extension is PAC, Israel Journal of Mathematics, vol. 85 (1994), no. 1-3, pp. 199–202.Google Scholar
[30] Ehud, Hrushovski and Boris, Zilber, Zariski geometries, Journal of the American Mathematical Society, vol. 9 (1996), no. 1, pp. 1–56.Google Scholar
[31] Thomas, Jech, Set Theory, The third millennium edition, revised and expanded. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Google Scholar
[32] Klaus, Kaiser, Über eine Verallgemeinerung der Robinsonschen Modell-vervollständigung, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 15 (1969), pp. 37–48.Google Scholar
[33] Akihiro, Kanamori, The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings, second ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Google Scholar
[34] Byunghan, Kim and Anand, Pillay, From stability to simplicity, The Bulletin of Symbolic Logic, vol. 4 (1998), no. 1, pp. 17–36.Google Scholar
[35] Serge, Lang, Algebra, second ed., Addison-Wesley Publishing Company, 1984.Google Scholar
[36] Serge, Lang and André, Weil, Number of points of varieties in finite fields, American Journal of Mathematics, vol. 76 (1954), pp. 819–827.Google Scholar
[37] Daniel, Lascar, Stability in Model Theory, Longman, New York, 1987.Google Scholar
[38] Angus, Macintyre, On ω1-categorical theories of fields, Polska Akademia Nauk. Fundamenta Mathematicae, vol. 71 (1971), no. 1, pp. 1–25, (errata insert).Google Scholar
[39] David, Marker, Model Theory, An introduction, Graduate Texts in Mathematics, vol. 217, Springer-Verlag, New York, 2002.Google Scholar
[40] M., Morley, Categoricity in Power, Transactions of the American Mathematical Society, vol. 114 (1965), pp. 514–538.Google Scholar
[41] David, Pierce and Anand, Pillay, A note on the axioms for differentially closed fields of characteristic zero, Journal of Algebra, vol. 204 (1998), no. 1, pp. 108–115.Google Scholar
[42] Anand, Pillay, An Introduction to Stability Theory, Oxford Logic Guides, vol. 8, Oxford University Press, New York, 1983.Google Scholar
[43] Anand, Pillay, The geometry of forking and groups of finite Morley rank, The Journal of Symbolic Logic, vol. 60 (1995), pp. 1251–1259.Google Scholar
[44] Anand, Pillay, Geometric Stability Theory, Oxford Logic Guides, vol. 32, Oxford University Press, New York, 1996.Google Scholar
[45] Bruno, Poizat, Cours de Théorie des Modèles, Nur Al-Mantiq Wal-Ma'rifah, Villeurbanne, 1985.Google Scholar
[46] Bruno, Poizat, Groupes Stables, Nur Al-Mantiq Wal-Mari'fah, Villeurbanne, 1987.
[47] Mike, Prest, Model Theory and Modules, London Mathematical Society Lecture Note Series, vol. 130, Cambridge University Press, Cambridge, 1988.Google Scholar
[48] Alex, Prestel and Charles N., Delzell, Mathematical Logic and Model Theory: A Brief Introduction, Universitext, Springer, 2011.Google Scholar
[49] V. A., Puninskaya, Vaught's conjecture, Journal of Mathematical Sciences (New York), vol. 109 (2002), no. 3, pp. 1649–1668, Algebra, 16.Google Scholar
[50] Gerald E., Sacks, Saturated Model Theory, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Reading, Mass., 1972.Google Scholar
[51] Igor R., Shafarevich, Basic Algebraic Geometry. 1, Varieties in projective space, second ed., Springer-Verlag, Berlin, 1994, Translated from the 1988 Russian edition and with notes by Miles Reid.
[52] Saharon, Shelah, Every two elementarily equivalent models have isomorphic ultrapowers, Israel Journal of Mathematics, vol. 10 (1971), pp. 224–233.Google Scholar
[53] Saharon, Shelah, Uniqueness and characterization of prime models over sets for totally transcendental first-order-theories, The Journal of Symbolic Logic, vol. 37 (1972), pp. 107–113.Google Scholar
[54] Saharon, Shelah, Classification Theory, North Holland, Amsterdam, 1978.Google Scholar
[55] Saharon, Shelah, On uniqueness of prime models, The Journal of Symbolic Logic, vol. 43 (1979), pp. 215–220.Google Scholar
[56] Saharon, Shelah, Simple unstable theories, Annals of Mathematical Logic, vol. 19 (1980), no. 3, pp. 177–203.Google Scholar
[57] Joseph R., Shoenfield, Mathematical Logic, Association for Symbolic Logic, Urbana, IL, 2001, Reprint of the 1973 second printing.Google Scholar
[58] Katrin, Tent, Very homogeneous generalized n-gons of finite Morley rank, Journal of the London Mathematical Society. Second Series, vol. 62 (2000), no. 1, pp. 1–15.Google Scholar
[59] Jouko, Väänänen, Barwise: abstract model theory and generalized quantifiers, The Bulletin of Symbolic Logic, vol. 10 (2004), no. 1, pp. 37–53.Google Scholar
[60] Frank, Wagner, Simple Theories, Kluwer Adacemic Publishers, Dordrecht, 2000.Google Scholar
[61] Frank O., Wagner, Stable Groups, London Mathematical Society Lecture Note Series, vol. 240, Cambridge University Press, Cambridge, 1997.Google Scholar
[62] John S., Wilson, Profinite Groups, London Mathematical Society Monographs. New Series, vol. 19, Oxford University Press, New York, 1998.Google Scholar
[63] Martin, Ziegler, Model theory of modules, Annals of Pure and Applied Logic, vol. 26 (1984), no. 2, pp. 149–213.Google Scholar
[64] Boris, Zilber, Strongly minimal countably categorical theories. II, III, Akademiya Nauk SSSR. Sibirskoe Otdelenie. Sibirskii Matematicheskii Zhurnal, vol. 25 (1984), no. 4, pp. 63–77.Google Scholar
[65] Boris, Zilber, Analytic and pseudo-analytic structures, Logic Colloquium 2000, Lecture Notes in Logic, vol. 19, Association for Symbolic Logic, Urbana, IL, 2005, pp. 392–408.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • REFERENCES
  • Katrin Tent, Martin Ziegler, Albert-Ludwigs-Universität Freiburg, Germany
  • Book: A Course in Model Theory
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139015417.016
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • REFERENCES
  • Katrin Tent, Martin Ziegler, Albert-Ludwigs-Universität Freiburg, Germany
  • Book: A Course in Model Theory
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139015417.016
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • REFERENCES
  • Katrin Tent, Martin Ziegler, Albert-Ludwigs-Universität Freiburg, Germany
  • Book: A Course in Model Theory
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139015417.016
Available formats
×