1st Semester 2024/25: Forcing and Independence Proofs
- Instructors
- Yurii Khomskii
- ECTS
- 6
- Description
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 universe, Martin's Axiom (without its consistency proof), the technical aspects of forcing, up until the construction of a model of ZFC + ¬CH.
- Organisation
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, the students give talks presenting a segment of the material. Successful evaluation of the project is be based on completion of the assignments and presentations.
- Prerequisites
Knowledge of Axiomatic Set Theory, until at least ordinal and cardinal arithmetic and the Axiom of Choice. Basic knowledge of Model Theory (Tarski-Vaught criterion and Skolem Hull) is useful but not strictly necessary.
- Assessment
Successful evaluation of the project is be based on completion of the assignments and presentations.
- References
We will use the followint three textbooks, mostly following the first one:
- Kenneth Kunen, Set Theory (2011 edition).
- Kenneth Kunen, An Introduction to Independence Proofs (1980) (an older edition but better in some respects).
- Thomas Jech, Set Theory (2000 edition).