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 (6,267 words) - 22:43, 15 August 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...
41 KB (5,021 words) - 06:29, 26 July 2024
axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory. Abraham Adolf Halevi Fraenkel studied...
13 KB (1,420 words) - 23:45, 5 May 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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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
in axiomatic set theory by the axioms of Zermelo–Fraenkel set theory. Alternative set theories include: Vopěnka's alternative set theory Von Neumann–Bernays–Gödel...
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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
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 (4,747 words) - 09:15, 3 July 2024
about the notions of length, area and volume in formal set theory. In Zermelo–Fraenkel set theory, the axiom of choice entails that non-measurable subsets...
8 KB (1,201 words) - 18:26, 10 June 2024