Univalence as a New Principle of Logic

Speaker: Steve Awodey

Date: 2014

Location: PIMS, University of Calgary

Conference: The Calgary Mathematics & Philosophy Lectures

Subject: Mathematics, Logic and Foundations

Class: Scientific

Abstract:

It is often convenient or useful in mathematics to treat isomorphic structures as the same.  The Univalence Axiom for the foundations of mathematics elevates this idea to a foundational principle in the setting of Homotopy Type Theory.  It states, roughly, that isomorphic structures can be identified.  In his talk, Prof. Awodey will explain this principle and how it can be taken as an axiom, and explore the motivations and consequences, both mathematical and philosophical, of making such an assumption.