# Blog Archives

# Topic Archive: Gentzen

Model theory seminarFriday, March 21, 201412:30 pmGC 6417

# The consistency of Peano Arithmetic

University of Pennsylvania

In 1936, only a few years after the incompleteness theorems were proved, Gentzen proved the consistency of Peano arithmetic by using transfinite induction up to the ordinal epsilon_0. I will give a short proof of the result, based on on the simplification introduced by Schutte, and discuss some of the consequences.