# Metmathematics I

# Math 502/Phil 596

# Fall 2005

Course Meeting: 10:00 MWF 302 AH

Call Number: 22685/23110

Instructor: David Marker

Office: 411 SEO

Office Hours: M,W: 11-12, F:8:30-10:00

phone: (312) 996-3069

e-mail: marker@math.uic.edu

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

### Description

A first graduate course in mathematical logic.
We will introduce the fundamental themes of mathematical logic
(truth, provability, and computability), discuss their
interconnections and examine the power and limits of formal methods.
- 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
- Further topics in computability theory

Godel's Incompleteness Theorem will be discussed in Math 503 in Spring
semester. The sequence Math 502-503 leads to the logic prelim.
### Texts

- 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

For this course I will not be closely following any text.

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 bookstore told me they were having trouble with
Ebbinghaus-Flum-Thomas.
I have asked them to order the replacement*
- J. Shoenfield,
*Mathematical Logic*, A. K. Peters, 2001

*
Shoenfield is a classic text in the subject covering a great deal
of interesting material with wonderful problems. *

Unfortunately,
in some aspects it is old-fashioned and the notation can be very
cumbersome.
My presentation of material will
**not** closely follow Shoenfield.

I will circulate lecture notes.
### Prerequisites

Graduate standing. No previous background in logic is assumed. As many examples will come from Algebra, Math 516 is a useful corequisite.
### 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.
There will probably be a one hour final exam, possibly oral,
testing basic concepts,
definitions, and statements of theorems.
### Lecture Notes

### Homework Assignments

Last updated 11/22/05