# MATH 512: Advanced Topics in Logic

## Fall 2012

Instructor: Dima Sinapova

Class Meets: MWF 2:00 - 2:50 in LH 103

Office: 421 SEO

Office Hours: MW 11-12

phone: (312)-996-2371

e-mail: sinapova@math.uic.edu

### Description

I plan to cover stationary sets, large
cardinals, proper forcing and consistency of the proper forcing axiom (PFA). Here is a tentative breakdown of topics:
- The club filter and stationary sets: basic properties, stationary reflection, square and diamond;
the nonstationary ideal, forcing and stationary sets

- Large cardinals and forcing: lifting elementary embeddings, maaster conditions, Prikry forcing

- Iterated Forcing: direct and inverse limits, Easton support, Silver's theorem.

- Proper forcing: definition and properties, the Proper Forcing Axiom (PFA), consistency of PFA from a supercompact cardinal

### Homework and grading

There will be some homework assignments, which will be posted online.