Linked bibliography for the SEP article "The Early Development of Set Theory" by José Ferreirós
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Cited Works
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mesurables B”, Comptes Rendus Acad. Sci. Paris, 162:
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- Bernstein, Felix, 1908, “Zur Theorie der trigonometrischen
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- Bolzano, Bernard, 1851, Paradoxien des Unendlichen, Leipzig, Reclam; English translation London, Routledge, 1920. (Scholar)
- Borel, Émile, 1898, Leçons sur la théorie
des fonctions, Paris, Gauthier-Villars. 4th edn 1950
with numerous additions. (Scholar)
- Cantor, Georg, 1872, “Über die Ausdehnung eines Satzes
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- –––, 1883, Grundlagen einer allgemeinen
Mannigfaltigkeitslehre, Leipzig: B.G. Teubner. In Cantor 1932:
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Frage der Mannigfaltigkeitslehre”, Jahresbericht der
Deutschen Mathematiker Vereinigung, 1: 75–78. Reprinted in
Cantor 1932: 278–280. English translation in Ewald 1996:
vol.2. (Scholar)
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282–351. English translation in Cantor, Contributions to the
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1955. (Scholar)
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- Dauben, Joseph, 1979, Georg Cantor. His Mathematics and Philosophy of the Infinite, Cambridge, MA: Harvard University Press. (Scholar)
- Dedekind, Richard, 1871, “Über die Komposition der
binären quadratischen Formen”, Supplement X to G.L.
Dirichlet & R. Dedekind, Vorlesungen über
Zahlentheorie, Braunschweig: Vieweg. [Later editions as
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315–334. English translation in Ewald 1996: vol. 2. (Scholar)
- –––, 1876/77, “Sur la théorie des
nombres entiers algébriques”, Bulletin des Sciences
mathématiques et astronomiques, 1st series, XI
(1876): 278–293; 2nd series, I (1877): 17–41,
69–92, 144–164, 207–248. Separate edition, Paris:
Gauthier-Villars, 1977. English translation by J. Stillwell:
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Werke, R. Fricke, E. Noether & Ö. Ore (eds.),
Braunschweig: Vieweg, 3 vols. Reprint New York: Chelsea, 1969. (Scholar)
- Dedekind, R. & Heinrich Weber, 1882, “Theorie der
algebraischen Funktionen einer Veränderlichen”,
Journal für reine und angew. Mathematik, 92:
181–290; reprinted in Dedekind 1930/32 (Volume 1),
pp. 238–350; English translation by John Stillwell, Theory
of Algebraic Functions of One Variable, Providence: American
Mathematical Society and London Mathematical Society, 2012. (Scholar)
- Ebbinghaus, H. D., 2015, Ernst Zermelo: An approach to his
life and work, second edition, Berlin: Springer Verlag. (Scholar)
- Ewald, William B., 1996, From Kant to Hilbert: A source book in the foundations of mathematics, 2 volumes, Oxford: Oxford University Press. (Scholar)
- Feferman, Solomon, 1988, “Weyl vindicated: Das Kontinuum 70
years later”, reprinted in In the Light of Logic,
Oxford: Oxford University Press, 1998, chap. 13. (Scholar)
- Ferreirós, José, 1995, “‘What Fermented
in Me for Years’: Cantor’s Discovery of Transfinite
Numbers”, Historia Mathematica, 22: 33–42. (Scholar)
- –––, 1999, Labyrinth of Thought. A history of set theory and its role in modern mathematics, Basel: Birkhäuser. (Scholar)
- Frege, Gottlob, 1903, Grundgesetze der Arithmetik, vol. 2, Jena: Pohle. Reprint Hildesheim: Olms, 1966. (Scholar)
- Gödel, Kurt, 1933, “The present situation in the
foundations of mathematics”, in S. Feferman et al. (eds),
Collected Works, Vol. 3, Oxford University Press, pp.
45–53. (Scholar)
- –––, 1947, “What is Cantor’s
continuum problem?”, American Mathematical Monthly, 54.
Reprinted in S. Feferman et al. (eds), Collected Works, Vol.
2, Oxford University Press, pp. 176–187. (Scholar)
- Hallett, Michael, 1984, Cantorian Set Theory and Limitation of Size, Oxford: Clarendon. (Scholar)
- Hausdorff, Felix, 1914, Grundzüge der Mengenlehre,
Leipzig: Viet. Reprinted New York: AMS Chelsea Publishing, 1949.
Reprinted as Volume II of Hausdorff 2001–. The third edition
(1937) was translated into English, 1957, Set theory, New
York: AMS Chelsea Publishing.
online scan of Hausdorff 1914.
(Scholar)
- –––, 1916, “Die Mächtigkeit der
Borelschen Mengen”, Mathematische Annalen, 77(3):
430–437. In Hausdorff [2001-], vol. 3. doi:10.1007/bf01475871
(Scholar)
- –––, 2001–, Gesammelte Werke, 9
volumes, E. Brieskorn, W. Purkert, U. Felgner, E. Scholz et al.
(eds.), Berlin: Springer. (Scholar)
- van Heijenoort, Jean, 1967, From Frege to Gödel: A source book in mathematical logic, 1879–1931, Cambridge, MA: Harvard University Press. Reprint as paperback, 2000. (Scholar)
- Kanamori, Akihiro, 1995, “The emergence of descriptive set
theory”, Synthese, 251: 241–262. . (Scholar)
- –––, 1996, “The mathematical development of set theory from Cantor to Cohen”, Bulletin of Symbolic Logic, 2: 1–71. (Scholar)
- Lavine, Shaughan, 1994, Understanding the Infinite, Cambridge, MA: Harvard University Press. (Scholar)
- Lebesgue, Henri, 1902, “Intégrale, longueur,
aire”, Annali di Matematica Pura ed Applicata, 7 (1):
231–359. (Scholar)
- –––, 1905, “Sur les fonctions
represéntables analytiquement”, Journal de
Mathématiques, (6e serie), 1: 139–216. (Scholar)
- Lusin, Nikolai, 1925, “Sur les ensembles projectifs de M.
Lebesgue”, Comptes Rendus Acad. Scie. Paris, 180:
1572–74. (Scholar)
- –––, 1930, Leçons sur les Ensembles
Analytiques et leurs Applications, with a preface by Lebesgue and
a note by Sierpinski, Paris: Gauthier-Villars. (Scholar)
- Mancosu, Paolo, 2009, “Measuring the Size of Infinite
Collections of Natural Numbers: Was Cantor’s Theory of Infinite
Number Inevitable?”, The Review of Symbolic Logic,
2(04): 612 – 646. (Scholar)
- Moore, Gregory H., 1982, Zermelo’s Axiom of Choice. Its
Origins, Development and Influence, Berlin: Springer. (Scholar)
- Moore, Gregory H. & A. Garciadiego, 1981,
“Burali-Forti’s Paradox: A reappraisal of its
origins”, Historia Mathematica, 8: 319–50. (Scholar)
- Moschovakis, Yiannis N., 1994, Set Theory Notes, New
York: Springer. (Scholar)
- Peckhaus, Volker & R. Kahle, 2002, “Hilbert’s
Paradox”, Historia Mathematica, 29 (2):
157–175. (Scholar)
- Purkert, Walter & H.J. Ilgauds, 1987, Georg Cantor
1845–1918, Basel: Birkhäuser. (Scholar)
- Rang, Bernhard & W. Thomas, 1981, “Zermelo’s
Discovery of the ‘Russell Paradox’”, Historia
Mathematica, 8: 15–22. (Scholar)
- Riemann, Bernhard, 1854/1868a, “Über die Hypothesen,
welche der Geometrie zu Grunde liegen” (Habilitationsvotrag),
Abhandlungen der Königlichen Gesellschaft der Wissenschaften
zu Göttingen, 13 (1868): 133–152. In Riemann 1892:
272–287. English translation by Clifford, reprinted in Ewald
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- –––, 1854/1868b, “Über die
Darstellbarkeit einer Function durch eine trigonometrische
Reihe”, (Habilitationsschrift), Abhandlungen der
Königlichen Gesellschaft der Wissenschaften zu
Göttingen, 13 (1868): 87–132. In Riemann 1892:
227–265. (Scholar)
- –––, 1892, Gesammelte mathematische Werke
und wissenschaftlicher Nachlass, H. Weber and R. Dedekind (eds.),
Leipzig, Teubner. Reprinted (together with the
Nachträge), M. Noether and W. Wirtinger (eds.), New
York: Dover, 1953. (Scholar)
- Russell, Bertrand, 1903, The Principles of Mathematics, Cambridge, University Press. Reprint of the 2nd edn. (1937): London: Allen & Unwin, 1948. (Scholar)
- Sierpiński, Waclav, 1918, “L’axiome de M. Zermelo
et son rôle dans la théorie des ensembles et
l’analyse”, Bulletin de l’Académie des
Sciences de Cracovie (Cl. Sci. Math. A), 99–152;
reprinted in Sierpiński, Oeuvres choisies, S. Hartman,
et al. (eds.), Volume 2, Warszawa: Editions scientifiques de Pologne,
1974.
- Sierpiński, Waclav & Alfred Tarski, 1930, “Sur une
propriété caractéristique des nombres
inaccessibles”, Fundamenta Mathematicae, 15:
292–300. (Scholar)
- Steinitz, Ernst, 1910, “Algebraische Theorie der
Körper”, Journal für die reine und angewandte
Mathematik, 137: 167–309. (Scholar)
- Suslin, Mikhail Ya., 1917, “Sur une définition des
ensembles measurables B sans nombres transfinis”, Comptes
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Paradox, second edition, Cambridge: Cambridge University
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- Vitali, G., 1905, Sul problema della misura dei gruppi di
punti di una retta, Bologna: Gamberini e Parmeggiani. (Scholar)
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- Tait, William W., 2000, “Cantor’s Grundlagen
and the Paradoxes of Set Theory”, Between Logic and
Intuition: Essays in Honor of Charles Parsons, G. Sher and R.
Tieszen (eds), Cambridge: Cambridge University Press, pp.
269–290. Reprinted in his The Provenance of Pure
Reason, Oxford: Oxford University Press, 2005, pp. 252–275.
(Scholar)
- Wang, Hao, 1974, “The concept of set”, in From
Mathematics to Philosophy, London, Routledge; reprinted in P.
Benacerraf & H. Putnam, Philosophy of Mathematics: selected
readings, Cambridge Univ. Press, 1983, 530–570. (Scholar)
- Zermelo, Ernst, 1904, “Beweis, dass jede Menge wohlgeordnet
werden kann”, Mathematische Annalen, 59: 514–516;
in Zermelo [2010], vol. 1, 80–119. English translation in van
Heijenoort 1967 (“Proof that every set can be
well-ordered”). (Scholar)
- –––, 1908, “Untersuchungen über die
Grundlagen der Mengenlehre”, Mathematische Annalen, 65:
261–281; ; in Zermelo [2010], vol. 1, 160–229. English
translation in van Heijenoort 1967 (“Investigations in the
foundations of set theory I”). (Scholar)
- –––, 2010–2011, Collected Works /
Gesammelte Werke, Vol. I and II, H.-D. Ebbinghaus et al. (eds.),
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Further Reading
- Cavaillès, Jean, 1962, Philosophie mathématique, Paris: Hermann. (Scholar)
- Ebbinghaus, Heinz-Dieter, 2007, Ernst Zermelo: An approach to
his life an work, New York: Springer. (Scholar)
- Fraenkel, Abraham, 1928, Einleitung in die Mengenlehre, 3rd edn. Berlin: Springer. (Scholar)
- Grattan-Guinness, Ivor (ed.), 1980, From the Calculus to Set
Theory, 1630–1910, London: Duckworth. (Scholar)
- Kanamori, Akihiro, 2004, “Zermelo and set theory”, Bulletin of Symbolic Logic, 10(4): 487–553. (Scholar)
- –––, 2007, “Gödel and set
theory”, Bulletin of Symbolic Logic, 13 (2):
153–188.
- –––, 2008, “Cohen and set theory”, Bulletin of Symbolic Logic, 14(3): 351–378. (Scholar)
- –––, 2009, “Bernays and set theory”, Bulletin of Symbolic Logic, 15(1): 43–60. (Scholar)
- Maddy, Penelope, 1988, “Believing the axioms”,
Journal of Symbolic Logic, 53(2): 481–511; 53(3):
736–764. (Scholar)
- Wagon, Stan, 1993, The Banach-Tarski Paradox, Cambridge:
Cambridge University Press. (Scholar)