Linked bibliography for the SEP article "Set Theory" by Joan Bagaria

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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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Asperó, D. and Schindler, R. D., 2021, “Martin’s Maximum\(^{++}\) implies Woodin’s Axiom \((\ast)\)”, Annals of Mathematics, 193(3): 793–835. (Scholar)
Bagaria, J., 2008, “Set Theory”, in The Princeton Companion to Mathematics, edited by Timothy Gowers; June Barrow-Green and Imre Leader, associate editors. Princeton: Princeton University Press. (Scholar)
Cohen, P.J., 1966, Set Theory and the Continuum Hypothesis, New York: W. A. Benjamin, Inc. (Scholar)
Enderton, H.B., 1977, Elements of Set Theory, New York: Academic Press. (Scholar)
Ferreirós, J., 2007, Labyrinth of Thought: A History of Set Theory and its Role in Modern Mathematics, Second revised edition, Basel: Birkhäuser. (Scholar)
Foreman, M., Magidor, M., and Shelah, S., 1988, “Martin’s maximum, saturated ideals and non-regular ultrafilters”, Part I, Annals of Mathematics, 127: 1–47. (Scholar)
Fremlin, D.H., 1984, “Consequences of Martin’s Axiom”, Cambridge tracts in Mathematics #84. Cambridge: Cambridge University Press. (Scholar)
Gödel, K., 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I,” Monatshefte für Mathematik Physik, 38: 173–198. English translation in Gödel 1986, 144–195. (Scholar)
–––, 1938, “The consistency of the axiom of choice and of the generalized continuum hypothesis”, Proceedings of the National Academy of Sciences, U.S.A. 24: 556–557. (Scholar)
–––, 1986, Collected Works I. Publications 1929–1936, S. Feferman et al. (eds.), Oxford: Oxford University Press. (Scholar)
Hauser, K., 2006, “Gödel’s program revisited, Part I: The turn to phenomenology”, Bulletin of Symbolic Logic, 12(4): 529–590.
Jech, T., 2003, Set theory, 3d Edition, New York: Springer. (Scholar)
Jensen, R.B., 1972, “The fine structure of the constructible hierarchy”, Annals of Mathematical Logic, 4(3): 229–308. (Scholar)
Kanamori, A., 2003, The Higher Infinite, Second Edition. Springer Monographs in Mathematics, New York: Springer. (Scholar)
Kechris, A.S., 1995, Classical Descriptive Set Theory, Graduate Texts in Mathematics, New York: Springer Verlag. (Scholar)
Kunen, K., 1980, Set Theory, An Introduction to Independence Proofs, Amsterdam: North-Holland. (Scholar)
Levy, A., 1960, “Axiom schemata of strong infinity in axiomatic set theory”, Pacific Journal of Mathematics, 10: 223–238. (Scholar)
–––, 1979, Basic Set Theory, New York: Springer. (Scholar)
Magidor, M., 1977, “On the singular cardinals problem, II”, Annals of Mathematics, 106: 514–547. (Scholar)
Martin, D.A. and R. Solovay, 1970, “Internal Cohen Extensions”, Annals of Mathematical Logic, 2: 143–178. (Scholar)
Martin, D.A. and J.R. Steel, 1989, “A proof of projective determinacy”, Journal of the American Mathematical Society, 2(1): 71–125.
Mathias, A.R.D., 2001, “Slim models of Zermelo Set Theory”, Journal of Symbolic Logic, 66: 487–496. (Scholar)
Neeman, I., 2002, “Inner models in the region of a Woodin limit of Woodin cardinals”, Annals of Pure and Applied Logic, 116: 67–155. (Scholar)
Scott, D., 1961, “Measurable cardinals and constructible sets”, Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, 9: 521–524. (Scholar)
Shelah, S., 1994, “Cardinal Arithmetic”, Oxford Logic Guides, 29, New York: The Clarendon Press, Oxford University Press. (Scholar)
–––, 1998, Proper and improper forcing, 2nd Edition, New York: Springer-Verlag. (Scholar)
Shelah, S. and W.H. Woodin, 1990, “Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable”, Israel Journal of Mathematics, 70(3): 381–394. (Scholar)
Solovay, R., 1970, “A model of set theory in which every set of reals is Lebesgue measurable”, Annals of Mathematics, 92: 1–56. (Scholar)
Solovay, R. and S. Tennenbaum, 1971, “Iterated Cohen extensions and Souslin’s problem”, Annals of Mathematics (2), 94: 201–245. (Scholar)
Todorcevic, S., 1989, “Partition Problems in Topology”, Contemporary Mathematics, Volume 84. American Mathematical Society. (Scholar)
Ulam, S., 1930, ‘Zur Masstheorie in der allgemeinen Mengenlehre’, Fundamenta Mathematicae, 16: 140–150. (Scholar)
Woodin, W.H., 1999, The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, De Gruyter Series in Logic and Its Applications 1, Berlin-New York: Walter de Gruyter. (Scholar)
–––, 2001, “The Continuum Hypothesis, Part I”, Notices of the AMS, 48(6): 567–576, and “The Continuum Hypothesis, Part II”, Notices of the AMS 48(7): 681–690. (Scholar)
Zeman, M., 2001, Inner Models and Large Cardinals, De Gruyter Series in Logic and Its Applications 5, Berlin-New York: Walter de Gruyter. (Scholar)
Zermelo, E., 1908, “Untersuchungen über die Grundlagen der Mengenlehre, I”, Mathematische Annalen 65: 261–281. Reprinted in Zermelo 2010: 189–228, with a facing-page English translation, and an Introduction by Ulrich Felgner (2010). English translation also in van Heijenoort 1967: 201–215. (Scholar)

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