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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)

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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
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NOTES

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