Math 574: Topics in Logic and Foundations

Spring 2004, MWF 9:05–9:55 AM, 113 McAllister, Schedule 292990 Stephen G. Simpson, 333 McAllister, 863-0775, simpson@math.psu.edu

The web page for this course is

    http://www.math.psu.edu/simpson/courses/math574/.

This course is intended for graduate students in mathematical logic. I will carefully introduce a variety of topics which are important in contemporary mathematical logic, but not normally covered in our basic logic sequence, MATH 557–558. Among the topics:

• computability in core mathematics

• unsolvable problems in core mathematics

• Turing degrees (i.e., degrees of unsovability)

• basis theorems and absoluteness

• combinatorial set theory

• ultrapowers

• large cardinals

• forcing

• infinite games and determinacy

• models of arithmetic

I don’t plan to go very deeply into any of these topics. Material will be selected from standard textbooks such as (1) Theory of Recursive Functions and Effective Computability, by Hartley Rogers, (2) Set Theory, by Thomas Jech, (3) Models of Peano Arithmetic, by Richard Kaye.