Zermelo set theory (sometimes denoted by Z-), as set out in a seminal paper in 1908 by Ernst Zermelo, is the ancestor of modern Zermelo–Fraenkel set theory...

antinomies de Russell et de Burali-Forti et le problème fundamental de la théorie des ensembles" and "Remarques sur la théorie des ensembles et les antinomies...

hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation...

regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty set A contains an element...

(1998), p. 807. Zermelo (1904). Zermelo (1908a). Burali-Forti (1897). Richard (1905). Zermelo (1908b). Ferreirós (2001), p. 445. Fraenkel (1922). Cohen...

Neumann's axiom. In 1930, Ernst Zermelo defined models of set theory satisfying the axiom of limitation of size. Abraham Fraenkel and Azriel Lévy have stated...

property J. König (1906). "Sur la théorie des ensembles". Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. 143: 110–112. Felix Hausdorff...

constructed by Robert M. Solovay (1970) in which all of the axioms of Zermelo–Fraenkel set theory (ZF) hold, exclusive of the axiom of choice, but in which...

antinomies de Russell et de Burali-Forti et le problème fundamental de la théorie des ensembles" and "Remarques sur la théorie des ensembles et les antinomies...

theorem and also to the axiom of choice, in the sense that within ZF (Zermelo–Fraenkel set theory without the axiom of choice) any one of the three is sufficient...

Mirimanoff, D. (1917), "Les antinomies de Russell et de Burali-Forti et le probleme fondamental de la theorie des ensembles", L'Enseignement Mathématique, 19:...

(NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which...

antinomy so far as we are concerned". But Zermelo's "definite criterion" is imprecise, and is fixed by Weyl, Fraenkel, Skolem, and von Neumann. In fact Skolem...

Machine The Comprehensive LaTeX Symbol List Bourbaki, N. (1970). Théorie des ensembles (in French). Paris: Hermann. ISBN 978-3-540-34034-8. Devlin, Keith...

91; Stewart & Tall 1977, p. 89 Bourbaki, Nicolas (1970). Théorie des ensembles. Éléments de mathématique. Springer. ISBN 9783540340348. Eccles, Peter...

http://www.mathpath.org/concepts/infinity.htm Bourbaki, N. (2006). Théorie des ensembles. Springer. pp. E II.34– E II.38. Kulik, B.; Fridman, A. (2022)....

91; Stewart & Tall 1977, p. 89 Bourbaki, Nicolas (1970). Théorie des ensembles. Éléments de mathématique. Springer. ISBN 9783540340348. Eccles, Peter...

to 1 or 0. Kuratowski, Casimir (1921). "Sur la notion de l'ordre dans la Théorie des Ensembles". Fundamenta Mathematicae. 2 (1): 161–171. doi:10.4064/fm-2-1-161-171...

resolved implicitly about twenty years later by Ernst Zermelo and Abraham Fraenkel. Zermelo–Fraenkel set theory provided a series of principles that allowed...

Dordrecht and London: Springer. pp. 59–221. Bourbaki, N. (1954). Théorie des ensembles. Paris: Hermann & Cie, Éditeurs. p. 14. Frege, G. (1879). Begriffsschrift...

Bourbaki, N. (1954). Théorie des ensembles (in French). Paris: Hermann & Cie, Éditeurs. p. 32. Chazal, G. (1996). Eléments de logique formelle. Paris:...

extralogical if set theory is set out axiomatically, as in the canonical Zermelo–Fraenkel set theory. Logical notions of higher order: While Tarski confined...

1007/978-3-319-51653-0. ISBN 978-3-319-51651-6. Bourbaki, N. (1954). Théorie des ensembles. Paris: Hermann & Cie, Éditeurs. p. 14. Edgington, Dorothy (2008)...