arXiv Open Access 2022

Univalent foundations and the equivalence principle

Benedikt Ahrens Paige Randall North

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Abstrak

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.

Topik & Kata Kunci

math.LO cs.LO math.HO

Penulis (2)

Benedikt Ahrens

Paige Randall North

Format Sitasi

APA MLA BibTeX

Ahrens, B., North, P.R. (2022). Univalent foundations and the equivalence principle. https://arxiv.org/abs/2202.01892

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Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓