Course Meeting: 9:00 MWF 310 AH

Call Number: 29841

Instructor: David Marker

Office: 404 SEO/ 312 SEO

Office Hours: (in 312 SEO) M, W 10:15-12:00

phone: (312) 413-3044

e-mail: marker@math.uic.edu

course webpage: http://www.math.uic.edu/~marker/math502-F15

- Mathematical structures
- Formal proofs
- Godel's Completeness Theorem
- The Compactness Theorem and elementary model theory
- Model theory of algebraically closed fields
- models of computation, Church's Thesis
- Universal machines and undecidability
- Recursively enumerable and arithmetic sets
- Godel's Incompleteness Theorem

- N. Cutland,
*Computability: An introduction to recursive function theory*, Cambridge University Press, 1986. - H.-D. Ebbinghaus, J. Flum and W. Thomas,
*Mathematical Logic*Second Edition, Springer-Verlag, 1994 - R. Kaye,
*Models of Peano Arithmetic*, Oxford University Press, 1991. - D. Marker,
*Model Theory: An Introduction*, Springer, 2012.

The treatment of material at the begining of the course on structures, truth and formal proofs will be similar to the treatment in Ebbinghaus-Flum-Thomas.

The treatment of computability will closely follow Cutland.

The treatment of Peano Arithmetic and Godel Incompleteness is similar to that of Kaye.

The treamtment of model theory follows early sections of my model theory book.

I will circulate lecture notes (see below).

- Course Lecture Notes
- Supplementary Notes on Quantifier Elimination
- Supplementary Notes on Incomparable Turing Degrees
- Basic Set Theory

### Problem Sets

- Problem Set 1 Due: Friday September 4.
- Problem Set 2 Due: Monday September 14
- Problem Set 3 Due: Wednesday September 23
- Problem Set 4 Due: Friday October 3
- Problem Set 5 Due: Monday October 12
- Problem Set 6 Due: Monday October 24
- Problem Set 7 Due: Monday November 23
- Problem Set 8 Due: Wednesday December 9