Zermelo-Fraenkel Set Theory

The language has no operation symbols and one binary predicate There will be 9 sentences of the theory (axioms) A model of ZF we denote by So is a non-empty set with an interpretation of as a subset of Elements of will be called ‘sets’ If is in then say ’ is a member of ’ or ’ belongs to ’ will be called the ‘universe of sets’ Axioms of ZF

Transitive Principle of Epsilon-Induction Epsilon-recursion Theorem Well-Founded Local Extensional Mostowski’s Collapsing Theorem Picture of the Universe