Fall 2012 and Winter 2013
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.
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:
Grades will be based on homework assignments and class participation.