# Skolem Lecture 2013

This years Skolem Lecture will be by Peter Aczel from The University of Manchester:

The Structure Identity Principle in Set Theory and Type Theory.

Title: The Structure Identity Principle in Set Theory and Type Theory.

Abstract: The Structure Identity Principle (SIP) states that

Isomorphic structures are structurally identical. After discussing

SIP in the setting of set-theoretical mathematical practice and

formulating a precise general notion of mathematical structure I will

prove a theorem of Homotopy Type Theory. The theorem states that a

strong form of SIP for that notion of mathematical structure, as

represented in intensional dependent type theory, is a consequence of

a new axiom for type theory, Voevodsky's Univalence Axiom. The strong

form of SIP expresses that isomorphic structures are identical.