Implicative Assemblies

Félix Castro; Alexandre Miquel; Krzysztof Worytkiewicz

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arXiv · 2304.10429

Implicative Assemblies

Félix Castro·Alexandre Miquel·Krzysztof Worytkiewicz

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Abstract

Implicative algebras, recently discovered by Miquel, are combinatorial structures unifying classical and intuitionistic realizability as well as forcing. In this paper we introduce implicative assemblies as sets valued in the separator of an underlying implicative algebra. Given a fixed implicative algebra A, implicative assemblies over A organise themselves in a category Asm with tracked set-theoretical functions as morphisms. We show that Asm is a quasitopos with NNO.

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Félix Castro, Alexandre Miquel, Krzysztof Worytkiewicz. 2023-04-20. Implicative Assemblies. https://arxiv.org/abs/2304.10429

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