Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Castro, Félix, Miquel, Alexandre, Worytkiewicz, Krzysztof
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4366735640