**Math 267 - Set Theory - Winter&Spring 2001
Course Homepage**

**Instructor:** Sam Buss, sbuss@ucsd.edu

**Spring quarter schedule: ** MWF 1:25-2:15. APM
6218.

**Syllabus: **

**(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....