1st Semester 2023/24: Forcing and Independence Proofs
- Yurii Khomskii
The aim of this project is to study the theory of forcing and independence proofs, including basic principles of models of set theory, absoluteness and reflection theorems, the constructible sets, Martin's Axiom (without its consistency proof), the technical aspects of forcing, and up till the original application of forcing which establishes the consistency of ZFC + ¬CH.
The students will study the material independently, assisted by several group meetings. There will be a four assignments to complete and submit. In the last week of January, students will give talks presenting a segment of the material.
Sufficient knowledge of axiomatic set theory up until and including ordinal and cardinal arithmetic and the axiom of choice. Familiarity with basic techniques from mathematical logic such as the Löwenheim-Skolem theorem.
Successful evaluation of the project is based on completion of the assignments and the presentations (pass/fail).
- Kenneth Kunen, Set Theory (2011 edition).
- Kenneth Kunen, An Introduction to Independence Proofs (1980) (an older version but better in some respects).
- Thomas Jech, Set Theory (2000 edition).