Implicative models of set theory

Samuele Maschio; Alexandre Miquel

doi:10.46298/entics.12426

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arXiv · 2310.10576

Implicative models of set theory

Samuele Maschio·Alexandre Miquel

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Abstract

In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence that any topos which is obtained from a Set-based tripos as the result of the tripos-to-topos construction hosts a model of intuitionistic or classical set theory, provided a large enough strongly inaccessible cardinal exists.

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Samuele Maschio, Alexandre Miquel. 2023-10-16. Implicative models of set theory. https://doi.org/10.46298/entics.12426

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