ZF

Definition

Initialism of Zermelo-Fraenkel (set theory): a particular axiomatic formulation of set theory without the axiom of choice.

Example Sentences

• "Gödel's model is an example of a simple type of inner model that might be called a definable transitive inner model³), where the universe is replaced by a transitive subuniverse defined within ZF, the membership relation is just the original one restricted to the subuniverse, and where the axioms of ZF relativized to the subuniverse, are provable within ZF."
• "1971, Ulrich Felgner, Models of ZF-Set Theory, Springer, Lecture Notes in Mathematics 223, page 21, 1. Corollary: ZF is not finitely axiomatizable. 2. Corollary: ZF is reflexive (i.e. the consistency of every finite subtheory of ZF can be proved within ZF)."
• "1991 [Kluwer Academic], Fred Landman, Structures for Semantics, 1991, Springer, Softcover, page 56, However, the problem with it, and the reason why it is not part of ZF strictly (apart from the fact that it implies the axiom of choice) is that it is rather arbitrary."