# MATH 512 Advanced Topics in Logic: Forcing and Large Cardinals

## Spring 2017

Instructor: Dima Sinapova

Class Meets: MWF 2:00 - 2:50 in TH 320

Office: 421 SEO

Office Hours: Mon 1pm, Wed 11am

phone: (312)-996-2371

e-mail: sinapova@math.uic.edu

### 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.