Implicative models of set theory

Implicative models of set theory

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...

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Veröffentlicht in:arXiv.org 2023-11
Hauptverfasser: Maschio, Samuele, Miquel, Alexandre
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Computer Science - Logic in Computer Science
Mathematics - Logic
Set theory
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description 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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title Implicative models of set theory
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