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Mathematics > Logic

arXiv:2202.01892 (math)
[Submitted on 3 Feb 2022]

Title:Univalent foundations and the equivalence principle

Authors:Benedikt Ahrens, Paige Randall North
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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 \in 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.
Subjects: Logic (math.LO); Logic in Computer Science (cs.LO); History and Overview (math.HO)
Cite as: arXiv:2202.01892 [math.LO]
  (or arXiv:2202.01892v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2202.01892
Journal reference: In: Centrone S., Kant D., Sarikaya D. (eds) Reflections on the Foundations of Mathematics. Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science), vol 407. 2019. Springer, Cham
Related DOI: https://doi.org/10.1007/978-3-030-15655-8

Submission history

From: Benedikt Ahrens [view email]
[v1] Thu, 3 Feb 2022 22:58:40 UTC (14 KB)
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