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