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Set theory

Prof. Monk

Fall 2013

Chapter 0: table of contents (occasionally updated)

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