Univalent Foundations and the Equivalence Principle

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • Ohio State University

Abstract

In this paper, we explore the ‘equivalence principle’ (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the kinds of objects under consideration. In set theoretic foundations, EP may not always hold: for instance, the statement
‘1 ∈ N’ is not invariant under isomorphism of sets. In univalent foundations, on the other hand, EP has been proven for many mathematical structures. We first give an overview of earlier attempts at designing foundations that satisfy EP. We then describe how univalent foundations validates EP.

Details

Original languageEnglish
Number of pages15
JournalSynthese
Publication statusAccepted/In press - 28 Jul 2018