Set Theory

1.

Axiomatic set theory. The systems ZF and ZFC. Relations between sets and classes.

2.

Principles of transfinite induction and recursion, and applications.

3.

The definitions of ordinal and cardinal numbers. Cardinal and ordinal arithmetic with and without the Generalized Continuum Hypothesis.

4.

Natural models of set theory and parts thereof. Reflection principles.

5.

Transfinite trees, closed unbounded and stationary sets.