Zermelo set theory information

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...

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...

of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem. Furthermore...

Non-well-founded set theory, which rejects set induction. The theory also constitutes a presentation of Zermelo–Fraenkel set theory Z F {\displaystyle...

theory Naive set theory S (set theory) Kripke–Platek set theory Scott–Potter set theory Constructive set theory Zermelo set theory General 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...

Z Zermelo set theory without the axiom of choice ZC Zermelo set theory with the axiom of choice Zermelo 1.  Ernst Zermelo 2.  Zermelo−Fraenkel set theory...

variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel set theory, with or without...

universal set in set theories that include either Zermelo's axiom of restricted comprehension, or the axiom of regularity and axiom of pairing. In Zermelo–Fraenkel...

power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set x {\displaystyle x} the existence of a set P ( x...

case of Halmos' Naive Set Theory, which is actually an informal presentation of the usual axiomatic Zermelo–Fraenkel set theory. It is "naive" in that...

set theory Tarski–Grothendieck set theory Von Neumann–Bernays–Gödel set theory Zermelo–Fraenkel set theory Zermelo set theory Set (mathematics) Set-builder...

replacement Axiom of power set Axiom of regularity Axiom schema of specification See also Zermelo set theory. With the Zermelo–Fraenkel axioms above, this...

differs from Zermelo–Fraenkel set theory (ZF) in that it allows proper classes, that is, objects that are not sets, including a class of all sets. It replaces...

identifies two such functions.) In Zermelo set theory one can model the ramified type theory of PM as follows. One picks a set ι to be the type of individuals...

generalization of Zermelo's theorem about the determinacy of finite games. It was proved by Donald A. Martin in 1975, and is applied in descriptive set theory to show...

set can be well-ordered. In 1963 Paul J. Cohen showed that in Zermelo–Fraenkel set theory without the axiom of choice it is not possible to prove the existence...

three of these characterizations can be proven equivalent in Zermelo–Fraenkel set theory without the axiom of choice, but the equivalence of the third...

In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally...