MATH 512 Advanced Topics in Logic: Forcing and Large Cardinals
Instructor: Dima Sinapova
Class Meets: MWF 2:00 - 2:50 in TH 320
Office: 421 SEO
Office Hours: Mon 1pm, Wed 11am
Description I plan to cover large cardinals, iterated forcing, Prikry type forcing, and
applications to infinitary combinatorics, singular cardinals, square principles, and the tree property. Here is a tentative breakdown of topics:
- Mahlo cardinals, weakly compact cardinals, measurable cardinals. Stationary reflection and the tree property.
- More large cardinals: strongly compact, supercompact and applications to combinatorics of successors of singular cardinals.
- Forcing: basic definitions and examples including the Levy collapse, the Cohen poset, Prikry forcing. The square principle.
- Iterated Forcing: direct and inverse limits, Easton support, Laver's theorem to get an indestructible supercompact.
- Lifting elementary embeddings.
Homework and grading There will be homework assignments, which will be posted online.