Math 223S, Topics in Set Theory.

Instructor: Itay Neeman.
Office: MS 6334.
Email:
Phone: 794-5317.
Office hours: Mondays and Wednesdays, 1-2pm.

Time and Place: Mondays and Wednesdays, 2-3:15pm, in MS 5148.

Material: The technique of forcing was introduced by Cohen to prove the independence of the Continuum Hypothesis from the axioms of mathematics. The class will cover several applications of this technique:

• Iterated forcing, including the consistency of Martin's Axiom.
• Forcing with large cardinals, leading to the consitency of the failure of the Singular Cardinal Hypothesis.
• Forcing over models of determinacy, leading to the consistency of ZFC+$\delta^1_2 = \aleph_2$ (and in particular the consistency of a definable counterexample to the Continuum Hypothesis).

Text: We will use the book Set Theory, an Introduction to Independence Proofs, by Kenneth Kunen, for iterated forcing. For forcing over models of determinacy we will use the papers Two consequences of determinacy consistent with choice by Steel and Van-Wesep, and Some consistency results in ZFC using AD by Woodin.

Grading and assignments: Students will be asked to solve assigned questions from Kunen's book in the first part of the class. Grading will be based on the solutions.