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Math 771 Set Theory  MWF 2:25pm    Spring 2010

Prerequisite:  M770 or equivalent

Textbook:  None
Recommended Text: Kunen, Kenneth; Set theory. An introduction
to independence proofs. Studies in Logic and the Foundations
of Mathematics, 102. North-Holland Publishing Co.,
Amsterdam-New York, 1980. xvi+313 pp. ISBN: 0-444-85401-0 

DESCRIPTION:  This is a beginning course in set theory for
graduate students that already know something about the basic
material:
ordinals and cardinal arithmetic,
ZF (the Zermelo-Fraenkel axioms of set theory),
AC (the Axiom of Choice), and 
CH (the Continuum Hypothesis).

Two highlights of the course are:

Godel's Theorem:  If ZF is consistent, then so is ZF + AC + CH.
 
Cohen's Theorems: If ZF is consistent, then
so is ZF + AC + notCH and so is ZF + notAC.

Topics will include: Martin's Axiom, stationary sets,
delta-systems, Suslin and Aronszajn trees, diamond
principle, absoluteness and reflection, the constructible
universe, and forcing.