Implicative algebras II: completeness w.r.t. Set-based triposes

TL;DR

This paper proves that every Set-based tripos can be represented as an implicative tripos, establishing a completeness result in the context of categorical logic.

Contribution

It demonstrates that all Set-based triposes are implicative, providing a significant completeness result in the theory of triposes.

Findings

All Set-based triposes are implicative triposes

Establishes a completeness result for implicative algebras

Advances understanding of the relationship between triposes and implicative structures

Abstract

We prove that all Set-based triposes are implicative triposes.