Year: 2023
Type: article
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. Comment: arXiv admin note: substantial text overlap with arXiv:2301.11740
Authors: Samuele Maschio, Alexandre Miquel
Institutions: University of Padua, Universidad de la República de Uruguay
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4388940284