Univalent foundations and the equivalence principle
Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)
Colleges, School and Institutes
- Ohio State University
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.
|Title of host publication||Reflections on the Foundations of Mathematics|
|Editors||Stefania Centrone , Debora Kant, Deniz Sarikaya|
|Publication status||E-pub ahead of print - 12 Nov 2019|