Math 506 Model Theory I

Spring 2011

Instructor: David Marker
Class: MWF 9-9:50 215 TH
Office: 312 SEO
Office Hours: to be determined
phone: (312) 996-3044
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/math506s11

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
P. Rothmaller, Introduction to Model Theory (Algebra, Logic and Applications Volume 15)

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 pg 1-21 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 Wednesday January 19.
Problem Set 2 Due Wednesday February 2: Exercises 2.5.13, 2.5.14.
Problem Set 3 Due Friday February 18: Exercises 2.5.11, 2.5.15, 2.5.26, 3.4.3 (in 3.4.3 a) you may ignore the part about strong minimality and algebraic closure)
Problem Set 4 Due Friday March 4.
Problem Set 5 Due Friday March 18.
Problem Set 6 Due Wednesday April 6: Exercises 4.5.16 a)-h),j,k, 4.5.29, 4.5.31, 4.5.34 (As bonus problems you are welcome to try 4.5.35 and/or 4.5.38)
Problem Set 7 Due Wednesday April 20
Problem Set 8 Due Wednesday May 4: Exercises: 5.5.2, 5.5.4. Optional (but encouraged) 4.5.42, 5.5.6, 5.5.7, 6.6.5 [Note: in 6.6.5 b) R should be the 4-ary relation {(a,b,c,d): a+b=c+d}.]