2015 UCLA Logic Summer School:
Determinacy
Instructor: Sherwood Hachtman
Lectures: 9am-11am in MS 6201
Problem-solving sessions will be held in MS 6603.
Lecture Notes. Subject to change!
Exercises:
Day 1: Games, strategies, and determinacy.
Day 2: The Axiom of Choice; Clubs.
Day 3: Baire space and Cantor space.
Day 4: Polish spaces, pointclasses, and Borel sets.
Day 5: Universal sets and the hierarchy theorem.
Weekend 1: AD and the perfect set property.
Day 6: Long games; the Baire property.
Day 7: Tail sets. Wadge reduction and complete sets.
Day 8: Lipschitz degrees; Choice and Θ.
Day 9: Projective and analytic sets; The separation property.
Day 10: Trees, codes, co-analytic sets.
Weekend 2: Gale-Stewart without choice; The Wadge degrees.
Day 11: Ultrafilters and normal measures.
Day 12: Martin measure; unfolded games; Polish group actions.
Day 13: Borel chromatic numbers.
There might exist axioms so abundant in their verifiable consequences, shedding so much light upon a whole field, and yielding such powerful methods for solving problems (and even solving them constructively, as far as that is possible) that, no matter whether or not they are intrinsically necessary, they would have to be accepted at least in the same sense as any well-established physical theory.
— Kurt Gödel in What is Cantor's continuum problem?
(1964), in Kurt Gödel's Collected Works, Vol. II, Feferman, Solomon, Eds.