Math 504 Set Theory I

Spring 2002




Instructor: David Marker
Class: MWF 303 Adams Hall, 11-11:50 Office: 411 SEO
Office Hours: M,F 9:00-10:30 and by appointment
phone: (312) 996-3069
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/504.html

Description

In the first half of the century it was shown that most of mathematics can be formalized inside of set theory and that a simple set of axioms could be given so that every acceptable proof followed formally from these axioms. Godel's Incompleteness Theorem implies that there are mathematical truths not settled by these axioms. The most famous is the Continuum Hypothesis (CH) that asserts that there are no infinite sets of cardinality greater than the natural numbers but less than the real numbers.
This course will start by introducting the axioms for set theory and developing the basic theory of cardinals and ordinals. We will then begin looking at models of set theory and prove that the Continuum Hypothesis is neither provable nor refutable. The topics covered will include:

Texts

K. Kunen, Set Theory: An Introduction to Independence Proofs, North-Holland, 1979.

Prerequisites

Graduate standing. Some familiarity with the very basic notions from mathematical logic (Math 430 or 502) such as languages and models

Grading

  • I will give out about 8 problem sets. You may work together on homework problems (and I encourage you to do so), but when you turn in the problem you should acknowledge that you have worked together.

    Assignments


    Dave Marker's Home Page


    Last updated 3/1/02