MATH 512 Advanced Topics in Logic: Combinatorial Set Theory

Spring 2019

Instructor: Dima Sinapova

Class Meets: MWF 12:00 - 12:50 in TH 320
Office: 421 SEO
Office Hours: Mon 10am -12pm
phone: (312)-996-2371
e-mail: sinapova@uic.edu

Description

This course is on applications of forcing and large cardinals to infinitary combinatorics. We will start with an introduction to cardinal arithmetic, especially at singular cardinals, large cardinals, and forcing techniques. Then we will analyze their interactions with combinatorial principles like square, the tree property, and strengthenings of the tree property such as ITP. 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, strengthenings of the tree property with a focus on ITP

Forcing: basic definitions and examples including the Levy collapse, the Cohen poset, Prikry forcing.

Singular cardinal arithmetic: the connection between SCH and the tree property

Consistency results about the tree property and ITP

Homework and grading

There will be occasional homework assignments.