Advanced Set Theory
Axiomatic Set Theory (ZFC)
Ordinal Numbers
Successor and Limit Ordinals
Cardinal Numbers
Cardinality of Infinite Sets
Cantor's Theorem
Continuum Hypothesis
Axiom of Choice
Equivalents of Choice
Zorn's Lemma
applications of Zorn's Lemma
Consistency
Large Cardinals
Descriptive Set Theory
Study of definable subsets of Polish spaces (separable completely metrizable spaces). Borel sets, analytic sets, projective sets.