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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

Solutions to exercises in Chapter 9

Solutions to exercises in Chapter 10

Solutions to exercises in Chapter 11

Solutions to exercises in Chapter 12

Solutions to exercises in Chapter 13

Solutions to exercises in Chapter 14

Solutions to exercises in Chapter 15

Solutions to exercises in Chapter 16

Solutions to exercises in Chapter 17

Solutions to exercises in Chapter 18

Solutions to exercises in Chapter 19

Solutions to exercises in Chapter 20

Solutions to exercises in Chapter 21