Math 267 - Set Theory - Winter&Spring 2001
Instructor: Sam Buss, email@example.com
Spring quarter schedule: MWF 1:25-2:15. APM 6218.
(a) Zermelo-Fraenkel axioms, Ordinals, Cardinals, Transfinite Induction, Axiom of Choice, Continuum Hypothesis, Well-founded sets, Constructible sets, Consistency of AC+GCH. (last two topics may not get covered until the second quarter).
(b) Introduction to logic as needed. First-order logic, Completeness theorem, Model theory, Incompleteness theorem.
(c) Applications to the foundations of mathematics. Integers, reals, Dedekind cuts.
(d) Completeness theorems..
(e) Inompleteness theorems..
(f) Consistency of AC and GCH with ZF.
(g) Independence of AC and GCH from ZF.
Textbook: Set Theory: An introduction to independence proofs.
by Ken Kunen.
This book presumes an undergraduate course in set theory, so I will cover material in more depth than this book. The first quarter topics will be a superset of chapters I and III. The second quarter will cover material from Chapters IV-VII.
Other good set theory books for reference include: (I can lend you copies if you cannot find them otherwise)
Thomas Jech, Set Theory.
Judith Roitman. Introduction to Modern Set Theory.
Herb Enderton, Elements of Set Theory.
Paul Halmos, Naive Set Theory.
Keith Devlin, The Joy of Sets.
Workload/Grading: I will assign about 4 homeworks per week and ask you to turn in about two per week. The difficulty of the assignments will vary widely. There will probably be a final, perhaps take-home.
Assignments: Postscript format and pdf format.
Lecture topics outline: Postscript format and pdf format. Will be updated without notice....