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Univalent type theory and modular formalisation of mathematics

Presented by: 
Thierry Coquand Göteborgs Universitet
Date: 
Tuesday 27th June 2017 - 11:00 to 12:00
Venue: 
INI Seminar Room 2
Abstract: 
 In the first part of the talk, I will try to compare the way mathematical collectionsare represented in set theory, simple type theory, dependent type theory and finallyunivalent type theory. The main message is that the univalence axiom is a strongform of extensionality, and that extensionality axiom is important for modularisationof concepts and proofs. The goal of this part is to explain to people familiar to simpletype theory why it might be interesting to extend this formalism with dependent types and the univalence axiom. 
The second part will try to explain in what way we can see models of univalent typetheory as generalisations of R. Gandy’s relative consistency proof of the extensionalityaxioms for simple type theory.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons