Topics in Logic and the Foundations of Mathematics

Course Description: An introduction to proof theory. We will be interested in the following questions: Is every mathematical truth provable from the axioms? Are the axioms consistent? Does each provable statement have a simplest proof?

We will cover seminal results of Gentzen and Gödel that address these questions, including the equi-consistency of constructive and classical arithmetic, the Gödel incompleteness theorems, the cut-elimination theorem and its corollaries, and Gentzen’s consistency proof of arithmetic.

Syllabus

Class Time and Location: Tu Th 11:25am - 12:40pm in Rockefeller Hall 102

Office Hours: W 11am-1pm and F 10am - 11am in Goldwin Smith 322