Ackermann, Wilhelm [1956] Zur Axiomatik der Mengenlehre, Mathematische Annalen, vol. 131, pp. 336–345.CrossRefGoogle Scholar

Benacerraf, Paul and Putnam, Hilary [1983] Philosophy of mathematics. Selected readings, second ed., Cambridge University Press, Cambridge.Google Scholar

Bernays, Paul [1937] A system of axiomatic set theory—Part I, The Journal of Symbolic Logic, vol. 2, pp. 65–77, reprinted in Müller, [1976, pp. 1–13].CrossRefGoogle Scholar

Bernays, Paul [1941] A system of axiomatic set theory—Part II, The Journal of Symbolic Logic, vol. 6, pp. 1–17, reprinted in Müller, [1976, pp. 14–30].Google Scholar

[Bernays, Paul 1958] Axiomatic set theory, Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, with a historical introduction by Fraenkel, Abraham A..Google Scholar

Bolzano, Bernard [1851] Paradoxien des Unendlichen, C. H. Reclam, Leipig.Google Scholar

Boolos, George S. [1971]The iterative concept of set, The Journal of Philosophy, vol. 68, pp. 215–231, reprinted in Boolos [1998], pp. 13–29.Google Scholar

Boolos, George S. [1989] Iteration again, Philosophical Topics, vol. 17, pp. 5–21, reprinted in Boolos [1998], pp. 88–105.Google Scholar

[Boolos, George S. 1998] Logic, logic, and logic, Harvard University Press, Cambridge MA, edited by Jeffery, Richard.Google Scholar

Boolos, George S. [2000] Must we believe in set theory?, Between logic and intuition: Essays in honor ofCharles Parsons (Sher, Gila and Tieszen, Richard, editors), Cambridge University Press, Cambridge, preprinted in Boolos [1998, pp., 120–132], pp. 257–268.Google Scholar

Burali-Forti, Cesare [1897] Una questione sui numeri transfiniti, Rendiconti del circolo matematico de Palermo, vol. 11, pp. 154–164.Google Scholar

Burgess, John P. [2009] Putting structuralism in its place, on website: www.princeton.edu/~jburgess.Google Scholar

Cantor, Georg [1872] Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen, Mathematische Annalen, vol. 5, pp. 123–132.Google Scholar

Dawson, John W. [1997] Logical dilemmas: The life and work of Kurt Gödel, A. K. Peters, Wellesley, MA.Google Scholar

Dedekind, Richard [1857] Abriss einer Theorie der höheren Kongruenzen in bezug auf einen reellen Primzahl-Modulus, Journal für die Reine und Angewandte Mathematik, vol. 54, pp. 1–26, reprinted in Dedekind [1930–1932, vol. 1, pp. 40–67].Google Scholar

Dedekind, Richard [1872] Stetigkeit und irrationale Zahlen, F. Vieweg, Braunschweig, translated with commentary in Ewald [1996, pp. 765–779].Google Scholar

Dedekind, Richard [1888] Was sind und was sollen die Zahlen?, F. Vieweg, Braunschweig, third, 1911 edition translated with commentary in Ewald [1996, pp. 787–833].Google Scholar

Dedekind, Richard [1930–1932] Gesammelte mathematische Werke, F. Vieweg, Baunschweig, edited by Fricke, Robert, Noether, Emmy and Ore, Öystein; reprinted by Chelsea Publishing Company, New York, 1969.Google Scholar

Dirichlet, Gustav Lejeune [1863] Vorlesungen über Zahlentheorie, F. Vieweg, Braunschweig, edited by Dedekind, Richard; second edition 1871, third edition 1879.Google Scholar

Dirichlet, Gustav Lejeune [1889/1897] G. Lejeune Dirichlet's Werke, Reimer, Berlin.Google Scholar

Ebbinghaus, Heinz-Dieter [2007] Ernst Zermelo. An approach to his life and work, Springer, Berlin.Google Scholar

Ewald, William [1996] From Kant to Hilbert: A source book in the foundations of mathematics, Clarendon Press, Oxford. Google Scholar

Foreman, Matthew and Kanamori, Akihiro [2010] Handbook of set theory, Springer, Berlin.CrossRefGoogle Scholar

Fraenkel, Abraham A. [1921] Über die Zermelosche Begründung der Mengenlehre, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 30, pp. 97–98.Google Scholar

Fraenkel, Abraham A. [1922] Zu den Grundlagen der Cantor–Zermeloschen Mengenlehre, Mathematische Annalen, vol. 86, pp. 230–237.Google Scholar

Fraenkel, Abraham A. [1925] Untersuchungen über die Grundlagen der Mengenlehre, Mathematische Zeitschrift, vol. 22, pp. 250–273.Google Scholar

Fraenkel, Abraham A. [1967] Lebenskreise. Aus den Erinnerungen eines jüdischen Mathematikers, Deutsche Verlags-Anstalt, Stuttgart.Google Scholar

Friedman, Harvey M. [1971a] Higher set theory and mathematical practice, Annals of Mathematical Logic, vol. 2, pp. 325–357.Google Scholar

Friedman, Harvey M. [1971b] A more explicit set theory, Axiomatic set theory (Scott, Dana S., editor), Proceedings of Symposia in Pure Mathematics, vol. 13(1), American Mathematical Society, Providence, RI, pp. 49–65.Google Scholar

[1981] On the necessary use of abstract set theory, Advances in Mathematics, vol. 41, pp. 209–280.Google Scholar

Friedman, Harvey M. and Scedrov, Andrej [1985] The lack of definable witnesses and provably recursive functions in intuitionistic set theories, Advances in Mathematics, pp. 1–13.Google Scholar

Gödel, Kurt [1931] Über formal unentscheidbare Sätze der Principia Mathematica und verwandter System I, Monatshefte für Mathematik und Physik, vol. 38, pp. 173–198, reprinted and translated in Gödel, [1986, pp. 144–195].Google Scholar

Gödel, Kurt [1932] Über Vollständigkeit und Widerspruchsfreiheit, Ergebnisse eines mathematischen Kolloquiums, vol. 3, pp. 12–13, reprinted and translated in Gödel, [1986, pp. 24–27].Google Scholar

Gödel, Kurt [1933o] The present situation in the foundation of mathematics, printed in Gödel [1995, pp. 45–53].Google Scholar

Gödel, Kurt [1938] The consistency of the axiom of choice and of the generalized continuum-hypothesis, Proceedings of the National Academy of Sciences of the United States of America, vol. 24, pp. 556–557, reprinted in Gödel, [1990, pp. 26–27].CrossRefGoogle Scholar

Gödel, Kurt [1940] The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory, Annals of Mathematics Studies, vol. 3, Princeton University Press, Princeton, reprinted in Gödel, [1990, pp. 33–101].Google Scholar

Gödel, Kurt [1944] Russell's mathematical logic, The philosophy of Bertrand Russell (Schilpp, Paul A., editor), Library of Living Philosophers, vol. 5, Northwestern University, Evanston, IL, reprinted in Gödel, [1990, pp. 119–141].Google Scholar

Gödel, Kurt [1946] Remarks before the Princeton bicentennial conference on problems in mathematics, reprinted in Gödel [1990, pp. 150–153].Google Scholar

Gödel, Kurt [1986] Collected works: Publications 1929–1936, vol. I, Clarendon Press, Oxford, edited by Feferman, Solomon et al. Google Scholar

Gödel, Kurt [1990] Collected works: Publications 1938–1974, vol. II, Oxford University Press, New York, edited by Feferman, Solomon et al. Google Scholar

Gödel, Kurt [1995] Collected works: Unpublished essays and lectures, vol. III, Oxford University Press, New York, edited by Feferman, Solomon et al. Google Scholar

Gödel, Kurt [2003] Collected works: Correspondence A–G, vol. IV, Clarendon Press, Oxford, edited by Feferman, Solomon et al. Google Scholar

Goodman, Nicolas D. [1985] Replacement and collection in intuitionistic set theory, The Journal of Symbolic Logic, vol. 50, pp. 344–348.Google Scholar

Hallett, Michael [1984] Cantorian set theory and the limitation of size, Oxford Logic Guides, vol. 10, Clarendon Press, Oxford.Google Scholar

Hartogs, Friedrich [1915] Über das Problem der Wohlordnung, Mathematische Annalen, vol. 76, pp. 438–443.Google Scholar

Harward, A. E. [1905] On the transfinite numbers, Philosophical Magazine, vol. (6)10, pp. 439–460.Google Scholar

Hausdorff, Felix [1914] Grundzüge der Mengenlehre, de Gruyter, Leipzig.Google Scholar

Heck, Richard Jr. [1995] Definition by induction in Frege's Grungesetze der Arithmetik, Frege's philosophy of mathematics (Demopoulos, William, editor), Harvard University Press, Cambridge MA, pp. 295–333.Google Scholar

Hessenberg, Gerhard [1906] Grundbegriffe der Mengenlehre, Vandenhoeck and Ruprecht, reprinted from Abhandlungen der Fries'schen Schule, Neue Folge 1 (1906), pp. 479–706.Google Scholar

Hilbert, David [1900] Über den Zahlbegriff, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 8, pp. 180–184, translated with commentary in Ewald Ewald [1996, pp. 1092–1095].Google Scholar

Kanamori, Akihiro [2004] Zermelo and set theory, this Bulletin, vol. 10, pp. 487–553.Google Scholar

Kisin, Mark [2009] Moduli of finite flat group schemes, and modularity, Annals of Mathematics, pp. 1085–1180.Google Scholar

Kreisel, Georg [1980] Kurt Gödel, Biographical Memoirs of Fellows of the Royal Society, vol. 26, pp. 149–224, vol. 27 (1981), p. 697; vol. 28 (1982), p. 719.Google Scholar

Landau, Edmund [1930] Grundlagen der Analysis, Akademische Verlagsgesellschaft, Leipzig, translated as Foundations of analysis , Chelsea Publishing Company, 1951.Google Scholar

Levy, Azriel [1959] On Ackermann's set theory, The Journal of Symbolic Logic, vol. 24, pp. 154–166.CrossRefGoogle Scholar

Levy, Azriel [1960a] Axiom schemata of strong infinity in axiomatic set theory, Pacific Journal of Mathematics, vol. 10, pp. 223–238, reprinted in Mengenlehre, Wissensschaftliche Buchgesellschaft Darmstadt, 1979, pp. 238–253.Google Scholar

Levy, Azriel [1960b] Principles of reflection in axiomatic set theory, Fundamenta Mathematicae, vol. 49, pp. 1–10.CrossRefGoogle Scholar

Levy, Azriel [1968] On von Neumann's axiom system for set theory, American Mathematical Monthly, pp. 762–763.Google Scholar

Levy, Azriel [1974] Parameters in the comprehension axiom schemas of set theory, Proceedings of the Tarski symposium, Proceedings of Symposia in Pure Mathematics, vol. 25, American Mathematical Society, Providence, RI, pp. 309–324.Google Scholar

Levy, Azriel and Vaught, Robert L. [1961] Principles of partial reflection in the set theories of Zermelo and Ackermann, Pacific Journal of Mathematics, vol. 11, pp. 1045–1062.Google Scholar

Martin, D. Anthony [1975] Borel determinacy, Annals of Mathematics, vol. 102, pp. 363–371.Google Scholar

Martin, D. Anthony [1985] A purely inductive proof of Borel determinacy, Recursion theory (Nerode, Anil and Shore, Richard A., editors), Proceedings of Symposia in Pure Mathematics, vol. 42, American Mathematical Society, Providence, RI, pp. 303–308.Google Scholar

Mathias, Adrian R. D. [2001a] Slim models of Zermelo set theory, The Journal of Symbolic Logic, vol. 66, pp. 487–496.Google Scholar

Mathias, Adrian R. D. [2001b] The strength of Mac Lane set theory, Annals of Pure and Applied Logic, pp. 107–234.Google Scholar

Mathias, Adrian R. D. [2006] Weak systems of Gandy, Jensen and Devlin, Set theory: Centre de Recerca Matemática, Barcelona 2003–2004 (Bagaria, Joan and Todorcevic, Stevo, editors), Trends in Mathematics, Birkhäuser Verlag, Basel, pp. 149-224.Google Scholar

Mathias, Adrian R. D. [2007] A note on the schemes of replacement and collection, Archive for Mathematical Logic, vol. 46, pp. 43–50.Google Scholar

Mathias, Adrian R. D. [2010] Unordered pairs in the set theory of Bourbaki 1949, Archive for Mathematical Logic, vol. 94, pp. 1–10.Google Scholar

Mathias, Adrian R. D. [∞] Bourbaki and the scorning of logic, to appear.Google Scholar

McLarty, Colin [2010] What does it take to prove Fermat's last theorem? Grothendieck and the logic of number theory, this Bulletin, pp. 359–377.Google Scholar

[∞] Set theory for Grothendieck's number theory, www.cwru.edu/artsci/philo/Groth%20found26.pdf.Google Scholar

Meschkowski, Herbert and Nilson, Winfried [1991] Georg Cantor. Briefe, Springer, Berlin.Google Scholar

Mirimanoff, Dimitry [1917a] Les antinomies de Russell et de Burali-Forti et le probléme fondamental de la théorie des ensembles, L'Enseignement Mathématique, vol. 19, pp. 37–52.Google Scholar

Mirimanoff, Dimitry [1917b] Remarques sur la théorie des ensembles et les antinomies cantoriennes. I, L'Enseignement Mathématique, vol. 19, pp. 209–217.Google Scholar

Montague, Richard M. [1961] Fraenkel's addition to the axioms of Zermelo, Essays on the foundations of mathematics (Bar-Hillel, Yehoshua, Poznanski, E. I. J., Rabin, Michael O., and Robinson, Abraham, editors), Magnes Press, Jerusalem, dedicated to Professor A. A. Fraenkel on his 70th birthday, pp. 91–114.Google Scholar

Moore, Gregory H. [1976] Ernst Zermelo, A. E. Harward, and the axiomatization of set theory, Historia Mathematica, vol. 3, pp. 206–209.Google Scholar

Moore, Gregory H. and Garciadiego, Alejandro R. [1981] Burali-Forti's paradox: a reappraisal of its origins, Historia Mathematica, vol. 8, pp. 319–350.Google Scholar

Müller, Gert H. [1976] Sets and classes. On the work of Paul Bernays, Studies in Logic and the Foundations of Mathematics, vol. 84, North-Holland, Amsterdam.Google Scholar

Nyikos, Peter J. [1980] A provisional solution to the normal Moore space problem, Proceedings of the American Mathematical Society, pp. 429–435.Google Scholar

Pettigrew, Richard [2008] Platonism and Aristoteleanism in mathematics, Philosophia Mathematica, vol. 16, pp. 310–332.Google Scholar

Potter, Michael [2004] Set theory and its philosophy, Oxford University Press, Oxford.Google Scholar

Quine, Willard V. O. [1960] Work and object, MIT Press, Cambridge.Google Scholar

Rathjen, Michael [2005] Replacement versus collection and related topics in constructive Zermelo–Fraenkel set theory, Annals of Pure and Applied Logic, vol. 136, pp. 156–174.Google Scholar

Reimann, Jan and Slaman, Theodore A. [2010] Effective randomness for continuous measures, preprint.Google Scholar

Reinhardt, William N. [1970] Ackermann's set theory equals ZF, Annals of Mathematical Logic, vol. 2, pp. 189–249.Google Scholar

Robinson, Raphael M. [1937] The theory of classes, a modification of von Neumann's system, The Journal of Symbolic Logic, vol. 2, pp. 29–36.Google Scholar

Rudin, Mary Ellen [1971] A normal space X for which X × I is not normal, Fundamenta Mathematicae, vol. 73, pp. 179–186.Google Scholar

Russ, Steve [2004] The mathematical works of Bernard Bolzano, Oxford University Press, Oxford.Google Scholar

Scott, Dana S. [1974] Axiomatizing set theory, Axiomatic set theory (Jech, Thomas, editor), Proceedings of Symposia in Pure Mathematics, vol. 13(2), American Mathematical Society, Providence, RI, pp. 207–214.Google Scholar

Shoenfield, Joseph R. [1967] Mathematical logic, Addison-Wesley, Reading MA.Google Scholar

Shoenfield, Joseph R. [1977] Axioms of set theory, Handbook of mathematical logic (Barwise, K. Jon, editor), North-Holland, Amsterdam, pp. 321–344. Google Scholar

Sieg, Wilfried and Schlimm, Dirk [2005] Dedekind's analysis of number: systems and axioms, Synthèse, vol. 147, pp. 121–170.Google Scholar

Skolem, Thoralf [1923a] Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Veränderlichen mit unendlichem Ausdehnungsberich, Skrifter utgit av Videnskabsselskapets i Kristiania, I. Matematisk-naturvidenskabelig klasse, vol. 6, pp. 1–38, translated in van Heijenoort [1967, pp. 302–333].Google Scholar

Skolem, Thoralf [1923b] Einige Bermerkungen zur axiomatischen Begründung der Mengenlehre, Wissenschaftliche Vorträge gehalten auf dem Fünften Kongress der Skandinavischen Mathematiker in Helsingfors vom 4. bis 7. Juli 1922, Akademische Buchhandlung, Helsinki, translated in van Heijenoort [1967, pp. 290–301], pp. 217–232.Google Scholar

Tait, William W. [1998] Zermelo's conception of set theory and reflection principles, The philosophy of mathematics today (Schirn, Matthias, editor), Oxford University Press, Oxford, pp. 469–483.Google Scholar

van Heijenoort, Jean [1967] From Frege to Gödel: A source book in mathematical logic, 1879–1931, Harvard University Press, Cambridge MA, reprinted 2002.Google Scholar

von Neumann, John [1923] Zur Einführung der transfiniten Zahlen, Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae (Szeged), sectio scientiarum mathematicarum, vol. 1, pp. 199–208, reprinted in von Neumann [1961, pp. 24–33], translated in van Heijenoort [1967, pp. 346–354].Google Scholar

von Neumann, John [1925] Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik, vol. 154, pp. 219–240, Berichtigung John von Neumann [1925] Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik, vol. 154, pp. 219–240 155, 128; reprinted in von Neumann [1961, pp. 34–56]; translated in van Heijenoort [1967, pp. 393–413].Google Scholar

von Neumann, John [1928a] Die Axiomatisierung der Mengenlehre, Mathematische Zeitschrift, vol. 27, pp. 669–752, reprinted in von Neumann [1961, pp. 339–422].Google Scholar

von Neumann, John [1928b] Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre, Mathematische Annalen, vol. 99, pp. 373–391, reprinted in von Neumann [1961, pp. 320–338].Google Scholar

von Neumann, John [1929] Über eine Widerspruchfreiheitsfrage in der axiomatischen Mengenlehre, Journal für die Reine und Angewandte Mathematik, vol. 160, pp. 227–241, reprinted in von Neumann [1961, pp. 494–508].Google Scholar

von Neumann, John [1961] Collected works, vol. 1, Pergamon Press, New York, edited by Taub, Abraham H..Google Scholar

Wang, Hao [1974a] The concept of set, From mathematics to philosophy, Humanities Press, New York, reprinted in Benacerraf and Putnam [1983, 530–570], pp. 181–223.Google Scholar

Wang, Hao [1974b] From mathematics to philosophy, Humanities Press, New York.Google Scholar

Wang, Hao [1981] Popular lectures on mathematical logic, Van Nostrand Reinhold, New York.Google Scholar

Wang, Hao [1996] A logical journey: From Gödel to philosophy, The MIT Press, Cambridge, MA.Google Scholar

Whitehead, Alfred North and Russell, Bertrand [1913] Principia mathematica, vol. 3, Cambridge University Press, Cambridge.Google Scholar

Wiener, Norbert [1914] A simplification of the logic of relations, Proceedings of the Cambridge Philosophical Society, pp. 387–390, reprinted in van Heijenoort [1967, pp. 224–227].Google Scholar

Zarach, Andrzej M. [1996] Replacement ↛ collection, Gödel '96. Logical foundations of Mathematics, Computer Science and Physics—Kurt Gödel's legacy (Hájek, Petr, editor), LectureNotes in Logic, vol. 6, Springer, Berlin, pp. 307–322.Google Scholar

Zermelo, Ernst [1904] Beweis dass jede Menge wohlgeordnet werden kann, Mathematische Annalen, vol. 59, pp. 514–516, reprinted and translated in Zermelo [2010, pp. 114–119].CrossRefGoogle Scholar

Zermelo, Ernst [1908a] Neuer Beweis für die Moglichkeit einer Wohlordnung, Mathematische Annalen, vol. 65, pp. 107–128, reprinted and translated in Zermelo [2010, pp. 120–159].Google Scholar

Zermelo, Ernst [1908b] Untersuchungen über die Grundlagen der Mengenlehre I, Mathematische Annalen, vol. 65, pp. 261–281, reprinted and translated in Zermelo [2010, pp. 188–229].Google Scholar

Zermelo, Ernst [1909] Sur les ensembles finis et le principe de l'induction complète, Acta Mathematica, vol. 32, pp. 185–193, reprinted and translated in Zermelo [2010, pp. 236–253].Google Scholar

Zermelo, Ernst [1930a] Über das mengentheoretische Model, printed and translated in Zermelo [2010, pp. 446–453].Google Scholar

Zermelo, Ernst [1930b] Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre, Fundamenta Mathematicae, vol. 16, pp. 29–47, reprinted and translated in Zermelo [2010, pp. 400–431].Google Scholar

Zermelo, Ernst [2010] Collected works, vol. 1, Springer, Berlin, edited by Ebbinghaus, Heinz-Dieter and Kanamori, Akihiro.Google Scholar