Math 116c Set Theory: Forcing and Independence Proofs

Spring 2024

Textbook

There is no official textbook for the course. I will be loosely following the relevant chapters of Kunen's Set Theory: An Introduction to Independence Proofs (especially Chapter 7); I may also draw from other sources. NOTE: I will be following Kunen's first set theory book (first edition 1980, most recent edition 1992), not the one published in the 2000s. My lecture notes will be posted to Canvas regularly: you can find them in the Files tab on the lefthand navigation panel.

Course Description

Welcome to Math 116c! This course is a continuation of 116b. Our main topic is forcing, a general technique for proving consistency results in set theory. We will preview forcing by reviewing the concept of a partial order from 116b, reviewing the concept of a model of a first order theory from 116a, and discussing transitive models of set theory. We'll then dive into forcing itself. Topics to be covered include: names, generic extensions, the forcing theorem, forcing with finite partial functions, chain conditions and closure conditions, cardinal preservation in generic extensions, the independence of the continuum hypothesis from ZFC, and other independence results. Time permitting we may go through more sophisticated forcing constructions, including iterated forcing.

Lecture Notes

  1. Lecture 1
  2. Lecture 2
  3. Lecture 3
  4. Lecture 4
  5. Lecture 5
  6. Lecture 6
  7. Lecture 7
  8. Lecture 8
  9. Lecture 9
  10. Lecture 10
  11. Lecture 11
  12. Lecture 12
  13. Lecture 13
  14. Lecture 14
  15. Lecture 15
  16. Lecture 16
  17. Lecture 17
  18. Lecture 18
  19. Lecture 19
  20. Lecture 20

Homeworks

  1. HW1
  2. HW2
  3. HW3
  4. HW4