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...

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

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

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...

contributions of Abraham Fraenkel, Zermelo set theory developed into the now-standard Zermelo–Fraenkel set theory (commonly known as ZFC when including...

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...

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...

theory can be thought of as roughly the predicative part of Zermelo–Fraenkel set theory (ZFC) and is considerably weaker than it. In its formulation...

axiomatic set theory, such as Zermelo–Fraenkel set theory. The axiom defines what a set is. Informally, the axiom means that the two sets A and B are...

Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces...

iterative hierarchy. S has the important property that all axioms of Zermelo set theory Z, except the axiom of extensionality and the axiom of choice, are...

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...

Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo set theory and Zermelo–Fraenkel...

In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any...

In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which...

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...

mathematics; it is a model of Zermelo set theory, the axiomatic set theory originally developed by Ernst Zermelo in 1908. Zermelo set theory was successful precisely...

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...

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

interpretation of set theory in expressive type theories. Graph models exist for ZF and also set theories different from Zermelo set theory, such as non-well...

here applies also to two families of set theories: on the one hand, a range of theories including Zermelo set theory near the lower end of the scale and...

non-conservative extension of Zermelo–Fraenkel set theory (ZFC) and is distinguished from other axiomatic set theories by the inclusion of Tarski's axiom...

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...

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

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...

axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo–Fraenkel...

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...

infinite well-orderable sets. The existence of the Hartogs number was proved by Friedrich Hartogs in 1915, using Zermelo set theory alone (that is, without...

Hierarchy (mathematics) List of set theory topics Philosophy of mathematics S (Boolos 1989) Von Neumann universe Zermelo set theory ZFC George Boolos, 1971,...