# Math 502 Metmathematics I

# Fall 1999

### Instructor David Marker

- class meetings: MWF 10:00-10:50 304 TH
- Office: 411 SEO, 341 SEO
- e-mail: marker@math.uic.edu

### Office Hours

- Monday: 2:30-3:30 (411 SEO)
- Wednesday: 8:30-9:30 (411 SEO) and by appointment

### 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.
The main results will be Godel's Completeness and Incompleteness
Theorems and Tarski's decidability results for the real and complex
fields. Specific topics covered will include.
- Mathematical structures
- Formal proofs
- The Completeness Theorem
- The Compactness Theorem and elementary model theory
- Introduction to computability theory
- The Incompleteness Theorem
- Decidability results for real closed fields and algebraically closed fields

### Texts

Z. Adamowicz and P. Zbierski, Logic of Mathematics, A Modern Course of Classical Logic, Wiley-Interscience, 1997.
N. Cutland, Computability: An introduction to recursive function theory, Cambridge University Press, 1986.
### Prerequisites

Graduate standing. No previous background in logic is assumed. As many examples will come from Algebra, Math 516 is a useful.
### Grading

I will give out about 10 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 be a one hour final exam testing basic concepts, definitions, and statements of theorems. It will be given in class on Friday of the last week of classes.

### Homework Assignments

Dave Marker's Home Page