Math 502 Metmathematics I

Fall 2001

Instructor: David Marker
Office: 411 SEO
Office Hours: M, W: 9:00-10:30
phone: (312) 996-3069
e-mail: marker@math.uic.edu
course webpage: http://www.math.uic.edu/~marker/502.html

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

H.-D. Ebbinghaus, J. Flum and W. Thomas, Mathematical Logic Second Edition, Springer-Verlag, 1994.

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 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 testing basic concepts, definitions, and statements of theorems.

Homework Assignments

Problem Set 1
Problem Set 2 (Due Monday September 17)
Problem Set 3 (Due Monday October 1)
Problem Set 4 (Due Friday October 12)
Problem Set 5 (Due Wednesday October 24)
Problem Set 6 (Due Friday November 2)
Problem Set 7 (Due Friday November 30)

Dave Marker's Home Page