# 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

### Other links

Week-by-Week Syllabus

Last updated 11/24/08