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
especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory. Abraham Adolf Halevi Fraenkel studied mathematics at the...
13 KB (1,420 words) - 23:45, 5 May 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...
15 KB (2,240 words) - 08:41, 12 October 2024
hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation...
21 KB (2,809 words) - 09:08, 28 May 2024
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...
24 KB (2,942 words) - 17:56, 1 September 2024
the axiom of pairing is one of the axioms of Zermelo–Fraenkel set theory. It was introduced by Zermelo (1908) as a special case of his axiom of elementary...
7 KB (1,147 words) - 01:48, 9 February 2024
axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally, the axiom states that for...
4 KB (670 words) - 19:50, 8 November 2023
philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set...
11 KB (1,794 words) - 12:59, 16 October 2024
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...
47 KB (6,684 words) - 07:45, 6 March 2024
axiomatic systems were proposed in the early twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known...
42 KB (5,062 words) - 00:31, 12 October 2024