“Feferman’s completeness theorem”
Martedì 8 Aprile 2025, ore 15:00 - Aula 2AB40 - Michael Rathjen (University of Leeds)
Abstract
Feferman proved in 1962 that any arithmetical theorem is a consequence of a suitable transfinite iteration of uniform reflections. This result is commonly known as Feferman’s completeness theorem. The purpose of this talk is to give two new proofs of Feferman’s completeness theorem that, we hope, sheds new light on this mysterious and often overlooked result.
Moreover, one of the proofs furnishes sharp bounds on the order types of well-orders necessary to attain completeness.
This is joint work with Fedor Pakhomov and Dino Rossegger.
