Linked bibliography for the SEP article "Large Cardinals and Determinacy" by Peter Koellner

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

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  • Feferman, S., 1960, “Arithmetization of metamathematics in a general setting,” Fundamenta Metamathecae 49: 35–92. (Scholar)
  • –––, 1964, “Systems of predicative analysis,” Journal of Symbolic Logic 29: 1–39. (Scholar)
  • –––, 1991, “Reflecting on incompleteness,” Journal of Symbolic Logic 56: 1–49. (Scholar)
  • –––, 1999, “Does mathematics need new axioms?American Mathematical Monthly 106: 99–111. (Scholar)
  • –––, 2005, “Predicativity,” in S. Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford: Oxford University Press, pp. 590–624. (Scholar)
  • Ferreirós, J., 2007, Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics, second revised edn, Birkhäuser Verlag AG. (Scholar)
  • Foreman, M. and A. Kanamori, 2010, Handbook of Set Theory, Springer-Verlag. (Scholar)
  • Friedman, H. M., 2011, Boolean Relation Theory, Association of Symbolic Logic. Forthcoming. (Scholar)
  • Gödel, K., 1947, “What is Cantor's continuum problem?” reprinted in Gödel 1990, pp. 176–187. (Scholar)
  • –––, 1964, “What is Cantor's continuum problem?” reprinted in Gödel 1990, pp. 254–270. (Scholar)
  • –––, 1990, Collected Works, Volume II: Publications 1938–1974, Oxford University Press, New York and Oxford. (Scholar)
  • Jackson, S., 2010, “Structural consequences of AD,” in Foreman and Kanamori 2010. (Scholar)
  • Kanamori, A., 1995, “The emergence of descriptive set theory,” in J. Hintikka (ed.), From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics, Vol. 251 of Synthese Library, Kluwer, Dordrecht, pp. 241–262. (Scholar)
  • –––, 2003, The Higher Infinite: Large Cardinals in Set Theory from their Beginnings, Springer Monographs in Mathematics, second edn, Springer, Berlin. (Scholar)
  • Kechris, A. S., 1995, Classical Descriptive Set Theory, Vol. 156 of Graduate Texts in Mathematics, Springer-Verlag, New York. (Scholar)
  • Koellner, P., 2006, “On the question of absolute undecidability,” Philosophia Mathematica 14(2): 153–188. Revised and reprinted with a new postscript in Kurt Gödel: Essays for his Centennial, edited by Solomon Feferman, Charles Parsons, and Stephen G. Simpson. Lecture Notes in Logic, 33. Association of Symbolic Logic, 2009. (Scholar)
  • –––, 2009a, “On reflection principles,” Annals of Pure and Applied Logic 157(2–3): 206–219. Kurt Gödel Centenary Research Prize Fellowships. (Scholar)
  • –––, 2009b, “Truth in mathematics: The question of pluralism,“ in O. Bueno and Ø. Linnebo (eds), New Waves in Philosophy of Mathematics, New Waves in Philosophy, Palgrave Macmillan, pp. 80–116. (Scholar)
  • Koellner, P. and W. H. Woodin, 2010, “Large cardinals from determinacy,” in Foreman and Kanamori 2010. (Scholar)
  • Larson, P. B., 2004, The Stationary Tower: Notes on a Course by W. Hugh Woodin, Vol. 32 of University Lecture Series, American Mathematical Society. (Scholar)
  • Lindström, P., 2003, Aspects of Incompleteness, Vol. 10 of Lecture Notes in Logic, second edn, Association of Symbolic Logic. (Scholar)
  • Maddy, P., 1988a, “Believing the axioms I,” Journal of Symbolic Logic 53: 481–511. (Scholar)
  • –––, 1988b, “Believing the axioms II,” Journal of Symbolic Logic 53: 736–764. (Scholar)
  • –––, 2011, Defending the Axioms, Oxford: Oxford University Press. (Scholar)
  • Markov, A. A., 1962, “On constructive mathematics,” Trudy Matematicheskogo Instituta Imeni V. A. Steklova 67(8–14). Translated in American Mathematical Society Translations: Series 2, 98, 1–9. (Scholar)
  • Martin, D., 1998, “Mathematical evidence,” in H. G. Dales and G. Oliveri (eds), Truth in Mathematics, Clarendon Press, pp. 215–231. (Scholar)
  • Martin, D. A. and J. R. Steel, 1989, “A proof of projective determinacy,” Journal of the American Mathematical Society 2(1): 71–125.
  • Moschovakis, Y. N., 1980, Descriptive Set Theory, Studies in Logic and the Foundations of Mathematics, North-Holland Pub. Co. (Scholar)
  • Nelson, E., 1986, Predicative Arithmetic, number 32 in Princeton Mathematical Notes, Princeton University Press. (Scholar)
  • Parsons, C., 2000, “Reason and intuition,” Synthese 125: 299–315. (Scholar)
  • –––, 2008, Mathematical Thought and its Objects, Cambridge University Press. (Scholar)
  • Shelah, S., 2003, “Logical dreams,” Bulletin of the American Mathematical Society 40(2): 203–228. (Scholar)
  • Steel, J., 2000, “Mathematics needs new axioms,” Bulletin of Symbolic Logic 6(4): 422–433. (Scholar)
  • Tait, W. W., 1981, “Finitism,” Journal of Philosophy 78: 524–556. Reprinted in Tait 2005b. (Scholar)
  • –––, 2001, “Gödel's unpublished papers on foundations of mathematics,” Philosophia Mathematica 9: 87–126.
  • –––, 2005a, “Constructing cardinals from below,” in Tait 2005b, pp. 133–154. (Scholar)
  • –––, 2005b, The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History, Logic and Computation in Philosophy, Oxford University Press. (Scholar)
  • Visser, A., 1998, “An overview of interpretability logic,” Advances in modal logic, Vol. 1 (Berlin, 1996), Vol. 87 of CSLI Lecture Notes, Stanford: CSLI Publications, pp. 307–359. (Scholar)
  • Woodin, W. H., 1999, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, Vol. 1 of de Gruyter Series in Logic and its Applications, de Gruyter, Berlin. (Scholar)
  • –––, 2001a, “The continuum hypothesis, part I,” Notices of the American Mathematical Society 48(6): 567–576. (Scholar)
  • –––, 2001b, “The continuum hypothesis, part II,” Notices of the American Mathematical Society 48(7): 681–690. (Scholar)
  • –––, 2005a, “The continuum hypothesis,” in R. Cori, A. Razborov, S. Todorĉević and C. Wood (eds), Logic Colloquium 2000, Vol. 19 of Lecture Notes in Logic, Association of Symbolic Logic, pp. 143–197. (Scholar)
  • –––, 2005b, “Set theory after Russell: the journey back to Eden,” in G. Link (ed.), One Hundred Years Of Russell's Paradox: Mathematics, Logic, Philosophy, Vol. 6 of de Gruyter Series in Logic and Its Applications, Walter De Gruyter Inc, pp. 29–47. (Scholar)
  • –––, 2011, “Suitable extender models I,” Journal of Mathematical Logic 11(1–2): 101–339. (Scholar)

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