Metmathematics I
Math 502
Fall 2015
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
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
- Godel's Incompleteness Theorem
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
- R. Kaye, Models of Peano Arithmetic, Oxford University Press, 1991.
- D. Marker, Model Theory: An Introduction, Springer, 2012.
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 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).
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