1st Semester 2020/21: Set Theory: Forcing and Independence Proofs
- Yurii Khomskii
This project will cover the basic principles of independence proofs in set theory. It is meant for students who have a knowledge of basic set theory comparable to the contents of the Mastermath course "Set Theory".
We will cover:
- Models of set theory
- Relativization and Absoluteness
- Reflection Theorems
- Martin's Axiom
- The Forcing Method
- Consistency of ZFC + CH and ZFC + not-CH.
The project will involve students reading the relevant sections of a textbook, giving several presentations, and submitting worked-out problems.
The students will read through the relevant sections of the textbooks Kenneth Kunen, Set Theory (1980 edition and 2011 edition) and give several presentations of (some of) the material in class in addition to submitting worked-out problems.
Depending on the number of students, the regulations in place in January, and the students' prefernce, meetings may be held online or on location.
Completion of the Mastermath course "Set Theory" or a comparable background.
Presentations and handed in worked-out solutions.
Kenneth Kunen, Set Theory (2011)
Kenneth Kunen, An Introduction to Independence Proofs (1980)
Thomas Jech, Set Theory (2000)