Oliver Club

Sergei ArtemovGraduate Center, City University of New York
The Provability of Consistency

Thursday, September 5, 2019 - 4:00pm
Malott 532

We revisit the foundational question “Can consistency of a theory T be established by means of T?” The usual answer “No, by Gödel's Second Incompleteness Theorem" is based on two assumptions:
1. Gödel's internalized consistency formula is the only way to represent consistency.
2. Any contentual reasoning within T internalizes as a formal derivation in T.
We show that already for Peano arithmetic PA both of these assumptions are false. Furthermore, we offer a proof of PA-consistency by means of PA, and discuss the potential impact of these findings.

Refreshments will be served at 3:30 PM.