MATH 512: Advanced Topics in Logic
Spring 2013
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.