Math 116b Axiomatic Set Theory

Winter 2024

Textbook

There is no official textbook for the course. I will be loosely following the first few chapters of Kunen's Set Theory: An Introduction to Independence Proofs; I may also draw from other sources. My lecture notes will be posted to Canvas regularly: you can find them in the Files tab on the lefthand navigation panel.

Course Description

Prerequisites: Ma 5 or equivalent, or instructor's permission. Welcome to Math 116b! This course is an introduction to axiomatic set theory. Topics to be covered include the standard (ZFC) axioms of set theory, the concept of cardinality, well-orderings, ordinals and their arithmetic, transfinite induction and recursion, cardinals and their arithmetic, the continuum hypothesis and Suslin's problem, the tree property, clubs and the club filter, and, time permitting, Godel's contructible universe L.

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

Homeworks

  1. HW1
  2. HW2
  3. HW3
  4. HW4
  5. HW5