1st Semester 2022/23: Forcing and Independence Proofs
- Yurii Khomskii
The aim of this project is to study the theory of forcing and independence proofs in set theory, including basic principles of models of set theory, absoluteness, reflection theorems, constructible sets, Martin's Axiom (without consistency proof), the technical aspects of forcing and a simple application of forcing establishing the consistency of ZFC + ¬CH.
The students will study the material independently, assisted by regular meetings. There will be a few take-home assignments to complete. In the end of January/early February, students will give talks presenting some segment of the material.
Knowledge of set theory including ordinal and cardinal arithmetic, cofinality and the Axiom of Choice; some knowledge of models of set theory, absoluteness and reflection is beneficial.
Completion of the assignments and presentations (pass/fail).
We will mostly follow the textbook: Kenneth Kunen, Set Theory, 2011 Edition, and partially the older, 1980 edition.