Set theory (English Wikipedia)

Kanamori, Akihiro (1996), "The Mathematical Development of Set Theory from Cantor to Cohen", Bulletin of Symbolic Logic, 2 (1): 1–71, doi:10.2307/421046
Rang, B.; Thomas, W. (1981), "Zermelo's discovery of the "Russell Paradox"", Historia Mathematica, 8 (1): 15–22, doi:10.1016/0315-0860(81)90002-1
Rowe, David E. (2024), "On the Origins of Cantor's Paradox", The Mathematical Intelligencer, 46 (2): 102–116, doi:10.1007/s00283-022-10259-x
Moore, Gregory H.; Garciadiego, Alejandro (1981), "Burali-Forti's paradox: A reappraisal of its origins", Historia Mathematica, 8 (3): 319–350, doi:10.1016/0315-0860(81)90070-7
Kanamori, Akihiro (2004), "Zermelo and set theory", Bulletin of Symbolic Logic, 10 (4): 487–553, doi:10.2178/bsl/1102083759
Džamonja, Mirna (2017), "Set Theory and its Place in the Foundations of Mathematics: A New Look at an Old Question", Journal of Indian Council of Philosophical Research, 34 (2): 415–424, doi:10.1007/s40961-016-0082-6
Feferman, Solomon; Friedman, Harvey M.; Maddy, Penelope; Steel, John R. (2000), "Does Mathematics Need New Axioms?", Bulletin of Symbolic Logic, 6 (4): 401–446, doi:10.2307/420965
Ferreirós, José (1995), ""What Fermented in Me for Years": Cantor's discovery of transfinite numbers", Historia Mathematica, 22 (1): 33–42, doi:10.1006/hmat.1995.1003
Codd, E. F. (1970), "A Relational Model of Data for Large Shared Data Banks", Communications of the ACM, 13 (6): 377–387, doi:10.1145/362384.362685
Montague, Richard (1970), "Universal Grammar", Theoria, 36 (3): 373–398, doi:10.1111/j.1755-2567.1970.tb00434.x
Tarnita, Corina E.; Antal, Tibor; Ohtsuki, Hisashi; Nowak, Martin A. (2009), "Evolutionary dynamics in set structured populations", Proceedings of the National Academy of Sciences, 106 (21): 8601–8604, doi:10.1073/pnas.0903019106, PMC 2689033
Maddy, Penelope (1988), "Believing the Axioms. (2 parts)", The Journal of Symbolic Logic, 53 (2, 3): 481–511, 736–764, doi:10.2307/2274520
Evangeliou, Christos (1985), "Aristotle's Doctrine of Predicables and Porphyry's Isagoge", Journal of the History of Philosophy, 23 (1): 15–34, doi:10.1353/hph.1985.0004
Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen", Journal für die reine und angewandte Mathematik (in German), 1874 (77): 258–262, doi:10.1515/crll.1874.77.258, S2CID 199545885, retrieved 2013-01-31{{citation}}: CS1 maint: deprecated archival service (link)
Forster, T. E. (2008), "The iterative conception of set" (PDF), The Review of Symbolic Logic, 1: 97–110, doi:10.1017/S1755020308080064, S2CID 15231169
Nelson, Edward (November 1977), "Internal Set Theory: a New Approach to Nonstandard Analysis", Bulletin of the American Mathematical Society, 83 (6): 1165, doi:10.1090/S0002-9904-1977-14398-X
Awodey, Steve (2011), "From Sets to Types, to Categories, to Sets", in Sommaruga, Giovanni (ed.), Foundational Theories of Classical and Constructive Mathematics, The Western Ontario Series in Philosophy of Science, vol. 76, Dordrecht: Springer, pp. 113–125, doi:10.1007/978-94-007-0431-2_5, ISBN 978-94-007-0430-5
Ferro, Alfredo; Omodeo, Eugenio G.; Schwartz, Jacob T. (September 1980), "Decision Procedures for Elementary Sublanguages of Set Theory. I. Multi-Level Syllogistic and Some Extensions", Communications on Pure and Applied Mathematics, 33 (5): 599–608, doi:10.1002/cpa.3160330503
Adams, Stephen (October 1993), "Functional Pearls Efficient sets—a balancing act", Journal of Functional Programming, 3 (4): 553–561, doi:10.1017/S0956796800000885, ISSN 1469-7653, retrieved 12 April 2025

homotopytypetheory.org (Global: low place; English: low place)

Homotopy Type Theory: Univalent Foundations of Mathematics Archived 2021-01-22 at the Wayback Machine. The Univalent Foundations Program. Institute for Advanced Study.

jhu.edu (Global: 560^th place; English: 313^th place)

cs.jhu.edu

Riemann, Bernhard (1854), "Über die Hypothesen, welche der Geometrie zu Grunde liegen" [On the Hypotheses which lie at the Bases of Geometry] (PDF)

libretexts.org (Global: 4,683^rd place; English: 3,565^th place)

math.libretexts.org

"6.3: Equivalence Relations and Partitions", Mathematics LibreTexts, 2019-11-25, archived from the original on 2022-08-16, retrieved 2022-07-27

mathsisfun.com (Global: low place; English: low place)

"Introduction to Sets", www.mathsisfun.com, archived from the original on 2006-07-16, retrieved 2020-08-20

ncatlab.org (Global: low place; English: low place)

homotopy type theory at the nLab

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

Tarnita, Corina E.; Antal, Tibor; Ohtsuki, Hisashi; Nowak, Martin A. (2009), "Evolutionary dynamics in set structured populations", Proceedings of the National Academy of Sciences, 106 (21): 8601–8604, doi:10.1073/pnas.0903019106, PMC 2689033

projecteuclid.org (Global: 4,781^st place; English: 3,117^th place)

Zenkin, Alexander (2004), "Logic Of Actual Infinity And G. Cantor's Diagonal Proof Of The Uncountability Of The Continuum", The Review of Modern Logic, vol. 9, no. 30, pp. 27–80, archived from the original on 2020-09-22, retrieved 2025-01-04

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Cantor, Georg (1874), "Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen", Journal für die reine und angewandte Mathematik (in German), 1874 (77): 258–262, doi:10.1515/crll.1874.77.258, S2CID 199545885, retrieved 2013-01-31{{citation}}: CS1 maint: deprecated archival service (link)
Forster, T. E. (2008), "The iterative conception of set" (PDF), The Review of Symbolic Logic, 1: 97–110, doi:10.1017/S1755020308080064, S2CID 15231169

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Awodey, Steve (2011), "From Sets to Types, to Categories, to Sets", in Sommaruga, Giovanni (ed.), Foundational Theories of Classical and Constructive Mathematics, The Western Ontario Series in Philosophy of Science, vol. 76, Dordrecht: Springer, pp. 113–125, doi:10.1007/978-94-007-0431-2_5, ISBN 978-94-007-0430-5

stanford.edu (Global: 194^th place; English: 182^nd place)

plato.stanford.edu

Bagaria, Joan (January 31, 2023) [October 8, 2014], Zalta, Edward N.; Nodelman, Uri (eds.), "Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University, retrieved May 9, 2026
Ferreirós, José (December 3, 2025) [April 10, 2007], Zalta, Edward N.; Nodelman, Uri (eds.), "The Early Development of Set Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University, retrieved May 9, 2026
Ferreirós, José (2024), "The Early Development of Set Theory", in Zalta, Edward N.; Nodelman, Uri (eds.), The Stanford Encyclopedia of Philosophy (Winter 2024 ed.), Metaphysics Research Lab, Stanford University, retrieved 2025-01-04{{citation}}: CS1 maint: deprecated archival service (link)
Bagaria, Joan (2020), "Set Theory", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2020 ed.), Metaphysics Research Lab, Stanford University, retrieved 2020-08-20
Marquis, Jean-Pierre (August 29, 2019) [First published December 6, 1996], Zalta, Edward N.; Nodelman, Uri (eds.), "Category Theory", Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University, retrieved May 9, 2026
Rodych, Victor (Jan 31, 2018), "Wittgenstein's Philosophy of Mathematics", in Zalta, Edward N. (ed.), Stanford Encyclopedia of Philosophy (Spring 2018 ed.), ISSN 1095-5054, OCLC 429049174
Rodych 2018, §2.1: "When we prove a theorem or decide a proposition, we operate in a purely formal, syntactical manner. In doing mathematics, we do not discover pre-existing truths that were 'already there without one knowing' (PG 481)—we invent mathematics, bit-by-little-bit." Note, however, that Wittgenstein does not identify such deduction with philosophical logic; cf. Rodych §1, paras. 7-12.
Rodych 2018, §3.4: "Given that mathematics is a 'motley of techniques of proof' (RFM III, §46), it does not require a foundation (RFM VII, §16) and it cannot be given a self-evident foundation (PR §160; WVC 34 & 62; RFM IV, §3). Since set theory was invented to provide mathematics with a foundation, it is, minimally, unnecessary."
Rodych 2018, §2.2: "An expression quantifying over an infinite domain is never a meaningful proposition, not even when we have proved, for instance, that a particular number $n$ has a particular property."
Rodych 2018, §3.6.

web.stanford.edu

"Order Relations and Functions" (PDF), Web.stanford.edu, archived (PDF) from the original on 2022-07-27, retrieved 2022-07-29

time.com (Global: 84^th place; English: 63^rd place)

Taylor, Melissa August, Harriet Barovick, Michelle Derrow, Tam Gray, Daniel S. Levy, Lina Lofaro, David Spitz, Joel Stein and Chris (14 June 1999), "The 100 Worst Ideas Of The Century", TIME, archived from the original on 12 April 2025, retrieved 12 April 2025{{cite magazine}}: CS1 maint: multiple names: authors list (link)

web.archive.org (Global: 1^st place; English: 1^st place)

Zenkin, Alexander (2004), "Logic Of Actual Infinity And G. Cantor's Diagonal Proof Of The Uncountability Of The Continuum", The Review of Modern Logic, vol. 9, no. 30, pp. 27–80, archived from the original on 2020-09-22, retrieved 2025-01-04
"Introduction to Sets", www.mathsisfun.com, archived from the original on 2006-07-16, retrieved 2020-08-20
"set theory | Basics, Examples, & Formulas", Encyclopedia Britannica, archived from the original on 2020-08-20, retrieved 2020-08-20
"6.3: Equivalence Relations and Partitions", Mathematics LibreTexts, 2019-11-25, archived from the original on 2022-08-16, retrieved 2022-07-27
"Order Relations and Functions" (PDF), Web.stanford.edu, archived (PDF) from the original on 2022-07-27, retrieved 2022-07-29
Homotopy Type Theory: Univalent Foundations of Mathematics Archived 2021-01-22 at the Wayback Machine. The Univalent Foundations Program. Institute for Advanced Study.
Taylor, Melissa August, Harriet Barovick, Michelle Derrow, Tam Gray, Daniel S. Levy, Lina Lofaro, David Spitz, Joel Stein and Chris (14 June 1999), "The 100 Worst Ideas Of The Century", TIME, archived from the original on 12 April 2025, retrieved 12 April 2025{{cite magazine}}: CS1 maint: multiple names: authors list (link)

worldcat.org (Global: 4^th place; English: 4^th place)

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Kolmogorov, A.N.; Fomin, S.V. (1970), Introductory Real Analysis (Rev. English ed.), New York: Dover Publications, pp. 2–3, ISBN 0486612260, OCLC 1527264
Rodych, Victor (Jan 31, 2018), "Wittgenstein's Philosophy of Mathematics", in Zalta, Edward N. (ed.), Stanford Encyclopedia of Philosophy (Spring 2018 ed.), ISSN 1095-5054, OCLC 429049174
Adams, Stephen (October 1993), "Functional Pearls Efficient sets—a balancing act", Journal of Functional Programming, 3 (4): 553–561, doi:10.1017/S0956796800000885, ISSN 1469-7653, retrieved 12 April 2025

zbmath.org (Global: 2,089^th place; English: 1,141^st place)

Mendelson, Elliott (1973), Number Systems and the Foundations of Analysis, Academic Press, MR 0357694, Zbl 0268.26001
Jech, Thomas (2003), Set Theory, Springer Monographs in Mathematics (Third Millennium ed.), Berlin, New York: Springer-Verlag, p. 642, ISBN 978-3-540-44085-7, Zbl 1007.03002

Set theory (English Wikipedia)

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