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Math 506 Model Theory I

Fall 2008

Instructor: David Marker
Class: MWF 9-9:50 302 AH
Office: 312 SEO
Office Hours: M,W 11:00-12:00 (in 312 SEO or 411 SEO) and by appointment
phone: (312) 996-3044
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/math506

Description

This will be a first course in model theory. It can be used with Math 502 as a prelim sequence. The topics covered will include:

applications to algebra
types
prime, saturated and homogeneous models
indiscernibles
Morley's Categoricity Theorem
omega-stable theories

Texts

D. Marker, Model Theory: An Introduction, Springer 2002

Some other useful introductory books include:

C.C. Chang and H.J. Keisler, Model Theory
W. Hodges, Model Theory
W. Hodges, A Shorter Model Theory
B. Poizat, A Course in Model Theory

Prerequisites

Graduate standing. Math 502 or familiarity with basic concepts from logic: languages, models up through the Compacteness Theorem. We will frequently consider algebraic examples, so coregistration in graduate algebra is encouraged.

Students should be familiar with Chapter 1 pg1-21 and Section 2.1 of the text.

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.

I reserve the right to give an in-class final exam.

Assignments

Problem Set 1 Due Friday September 5
Problem Set 2 Due Wednesday September 24
Problem Set 3 Due Friday October 3
Problem Set 4 Due Wednesday October 14: Do Problems 4.5.13, 4.5.16 a)-h),j,k, 4.5.17, 4.5.29, 4.5.31
Problem Set 5 Due Monday November 3: Do Problems 4.5.21, 4.5.22 (hint: see 5.2.12), 4.5.26, 4.5.34, 4.5.45 (assume T is a complete theory with infinite models)
Problem Set 6 Due Friday November 21 Do Problems 5.5.2, 5.5.4, 5.5.6
Problem Set 7 Due Monday December 7 Do Problems 6.6.5, 6.6.8, 6.6.17b, 6.6.19