A tripos based on compact Hausdorff spaces

TL;DR

This paper constructs a tripos framework based on the category of compact Hausdorff spaces, enabling the free completion to an elementary topos, thus linking topology with categorical logic.

Contribution

It introduces a novel tripos structure derived from compact Hausdorff spaces and demonstrates its completion to an elementary topos.

Findings

Establishes a tripos from compact Hausdorff spaces

Shows the free completion to an elementary topos

Bridges topology and categorical logic

Abstract

The category of compact Hausdorff spaces is the base of tripos. As such it can be freely completed to an elementary topos.