## MATH 8714, Topics in Logic Prof. Monk Fall 2013

This course will actually be a first graduate course in set theory. No prior acquantance with set theory is assumed. The first half of the course will give a rigorous development of the basics, through the axiom of choice and ordinal and cardinal arithmetic. The second half will go into the independence of the continuum hypothesis from the standard axioms of set theory. Lecture notes are below; they will be added to as the semester progresses. There will not be any tests. In class I will indicate exercises to be turned in, and grades will be computed on the basis of solutions of these. Re-trying exercises is encouraged if your first attempt doesn't work. 50% correct is needed for an A, 25% for a B. For pass/fail, simply attending most of the time is sufficient.

UPDATED ON NOVEMBER 21, 2013 (assigned exercises for Chapter 14; solutions for exercises in Chapter 7)
UPDATED ON NOVEMBER 29, 2013 (solutions for exercises in Chapter 8)

## ASSIGNED EXERCISES:

Chapter 6: E6.7, E6.8, E6.9, E6.14, E6.15 (hint: use E6.8 for E6.9)
Chapter 7: E7.1, E7.5, E7.7, E7.8
Chapter 8: E8.10, E8.13, E8.14, E8.15
Chapter 9: E9.1, E9.2, E9.14, E9.17
Chapter 10: E10.1, E10.11, E10.15, E10.16
Chapter 11: E11.1, E11.2, E11.3, E11.10
Chapter 12: E12.2, E12.3, E12.6, E12.7
Chapter 13: E13.1, E13.2, E13.3, E13.5
Chapter 14: E14.3, E14.4, E14.5, E14.6

## NOTES

Chapter 1: First-order logic
Chapter 2: The axioms of set theory
Chapter 3: elementary set theory
Chapter 4: ordinals, I
Chapter 5: recursion
Chapter 6: ordinals, II
Chapter 7: the axiom of choice
Chapter 8: cardinal arithmetic
Chapter 9: Boolean algebras and forcing orders
Chapter 10: Models of set theory
Chapter 11: Generic extensions and forcing
Chapter 12: Independence of CH
Chapter 13: Linear orders
Chapter 14: Trees
Chapter 15: Clubs and stationary sets
Chapter 16: Infinite combinatorics
Chapter 17: Martin's axiom
Chapter 18: Large cardinals
Chapter 19: Constructible sets
Chapter 20: Powers of regular cardinals
Chapter 21: Isomorphisms and negation of AC
Chapter 22: Embeddings, iterated forcing, and Martin's axiom
Chapter 23: Various forcing orders
Chapter 24: Proper forcing
Chapter 25: More examples of iterated forcing
Chapter 26: Cofinality of posets
Chapter 27: Basic properties of PCF
Chapter 28: Main cofinality theorems
Index of symbols (occasionally updated)
Index of words (occasionally updated)
Solutions to exercises in Chapter 1
Solutions to exercises in Chapter 3
Solutions to exercises in Chapter 4
Solutions to exercises in Chapter 5
Solutions to exercises in Chapter 6
Solutions to exercises in Chapter 7
Solutions to exercises in Chapter 8