Syllabus is provisional and may change based on the background and interests of the students.

1. Applications of transfinite induction and recursion, including constructions of geometrically interesting subsets of Euclidean space

2. Applications of the Axiom of Choice and its relatives: de Bruijn-Erdős theorem, Nielsen-Schreier theorem, existence of non-measurable sets, existence of algebraic closures

3. Applications of ultrafilters and ultraproducts: Arrow's Impossibility Theorem, Ax-Grothendieck theorem

4. Further applications to abelian group theory: Constructions of almost free nonfree groups, slender groups

5. Infinite games