Axiomatic Set Theory
Fall 2024
Instructor: Dima Sinapova
Class Meets: M W 2:00 - 3:20 in Hill 423
Office: Hill 230
Office Hours:
e-mail: dima.sinapova@rutgers.edu
Description
This is a first graduate course in set theory. The primary goal is to show the independence of the continuum hypothesis (CH).
We will cover the axioms of set theory (ZFC), ordinals, cardinals, the Constructible Universe L, and the proof that ZFC+CH holds in L. Then we will go over the method of forcing and use it to show the consistency
of not CH. Finally, we will discuss other applications of forcing, for example, Prikry type forcing, forcing iterations, and forcing axioms.
Here is a tentative breakdown of topics:
- Ordinals and cardinals. Cardinal arithmetic, ZFC axioms
- Godels' Constructible Universe L.
- Forcing I: basic definitions and examples including the Levy collapse, the Cohen poset, Prikry forcing. Iterated forcing
- Forcing II: further applications, Prikry forcing, Iterated forcing, MA, the Suslin hypothesis
Text:
- None required - the class notes will be enough. As a supplementary reading and reference, see Kenneth Kunen, Set Theory, College Publications, 2011.
Homework and grading
There will be regular homework assignments, which will be posted online. The grade will be based on the homework.