In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...
46 KB (6,252 words) - 21:13, 11 October 2024
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...
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century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly employed...
42 KB (5,062 words) - 00:31, 12 October 2024
work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize...
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axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory. Abraham Adolf Halevi Fraenkel studied...
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Von Neumann universe (redirect from Rank (set theory))
the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation...
21 KB (2,809 words) - 09:08, 28 May 2024
Such set theories are motivated by notions of closure in topology. The idea of a universal set seems intuitively desirable in the Zermelo–Fraenkel set theory...
10 KB (1,327 words) - 06:43, 21 May 2024
of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore...
11 KB (1,203 words) - 08:00, 20 August 2024
is only one empty set. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard...
41 KB (4,771 words) - 15:01, 8 October 2024
non-conservative extension of Zermelo–Fraenkel set theory (ZFC) and is distinguished from other axiomatic set theories by the inclusion of Tarski's axiom...
8 KB (1,036 words) - 00:22, 7 September 2024