**Math 260AB**

**Set Theory**

Fall 2012 and Winter 2013

**Instructor:**

Sam Buss

Email: sbuss@math.ucsd.edu

Office: APM 6210.

Office phone: 858-534-6455.

Cell phone: 858 then 442 then 2877.

Office hours (subject to change):
Tuesday 4:00-4:50, Wednesday 2:00-2:50, Friday 10:00-10:50.

**Overview:**
This course is an introduction to set theory at the graduate level.
There are no particular prerequisites beyond a certain level of mathematical
maturity. Topics to be covered during the Fall quarter include
axioms of ZFC set theory, a little foundations of mathematics,
ordinals, transfinite induction, cardinals, choice, constructibility,
and the consistency of the axiom of choice and the generalized continuum
hypothesis. Topics to be covered in the Winter quarter include
infinitary combinatorics, forcing, and the relative independence
of the axiom of choice and the continuum hypothesis.

**Course schedule:** MWF, 1:00-1:50pm, APM 7421.

**Textbook:**
The textbook is ** Set Theory**,
by Kenneth Kunen, 2011 edition. Please be sure to get the
correct edition, especially as it is available at very reasonable prices.

**Course PIAZZA web pages:** We will experiment with
using PIAZZA (piazza.com) for course announcements and discussions.
The course web page on piazza is at
piazza.com/ucsd/fall2012/math260a/home

**Handouts and course materials:**

If piazza will start working correctly, handouts will be available through piazza.com;
they are being placed here too.

Handout #1. Axioms of Set Theory.

Handout #2. Axioms and Rules of Inference for First-Order Logic.

Handout #3. J.R. Shoenfield, "Unramified Forcing",
in *Axiomatic Set Theory*, Proc. Symp. Pure Math., XIII, part I,
AMS, 1971, pp. 357-381,
is the source for the development of forcing as used in this course.
It is available here
as a PDF file.

**Homework assignments:**

Cumulative homework assignments. Do
approximately two problems per week, handing them in on Fridays.

The homework LaTeX source file is available too. For the
URL, replace the
filename extension ".pdf" with ".tex".

**Suggested reading and other resources:**

There are many excellent books and online resources for
set theory Here are a couple:

, by P.R. Halmos. This readable book manages to be both elementary and mathematically thorough at the same time. Recommended as a less advanced treatment of set theory than Kunen.**Naive Set Theory**-
by T. Jech. A comprehensive and advanced introduction to set theory. Now in a (substantially rewritten) third edition. Unfortunately, rather expensive to buy.**Set Theory**

**Grades** will be based on homework assignments
and class participation.