Notes on set theory
Don Monk
These are notes on advanced set theory, starting from basic principles. The
files are in pdf form. The table of contents and indices of words and symbols
will be revised as more chapters are added.
Table of contents
Chapter 1: The logic underlying set theory
Chapter 2: The axioms, and elementary set theory
Chapter 3: ordinals
Chapter 4: well-founded induction and recursion
Chapter 5: ordinal arithmetic
Chapter 6: cardinal arithmetic
Chapter 7: universes and relativization
Chapter 8: absoluteness, and the relative consistency of the non-existence of
inaccessibles
Chapter 9: generic extensions
Chapter 10: forcing, and ZFC in M[G]
Chapter 11: relative consistency of not(CH)
Chapter 12: constructibility, and the relative consistency of AC plus GCH
Chapter 13: clubs and stationary sets
Chapter 14: Martin's axiom
Chapter 15: embeddings, iterated forcing, and the relative consistency of MA
plus not(CH)
Chapter 16: powers of regular cardinals
Index of words
Index of symbols
Solutions to exercises in Chapter 1.
Solutions to exercises in Chapter 2.
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.