Aspects of Predicative Algebraic Set Theory I: Exact Completion

TL;DR

This paper introduces foundational concepts in Predicative Algebraic Set Theory, focusing on exact completion, to prepare for subsequent work on realizability and sheaf models within the framework.

Contribution

It establishes the initial groundwork for algebraic set theory, emphasizing exact completion, to support future developments in realizability and sheaf models.

Findings

Develops the concept of exact completion in algebraic set theory

Prepares the theoretical foundation for realizability models

Prepares the theoretical foundation for sheaf models

Abstract

This is the first in a series of three papers on Algebraic Set Theory. Its main purpose is to lay the necessary groundwork for the next two parts, one on Realisability and the other on Sheaf Models in Algebraic Set Theory.