Compactness in positive logic

TL;DR

This paper explores the concept of compactness within positive logic, providing a fundamental characterization of compactness in extensions and addressing questions posed by Poizat.

Contribution

It introduces a new perspective on compactness in positive logic, building on prior foundational work by Ben Yacov and Poizat.

Findings

Characterization of compactness in positive logic extensions

Clarification of the role of compact structures in positive logic

Addresses open questions posed by Poizat

Abstract

With the aim of developing the concepts of positive logic and in response to a question that was asked by Poizat in one of his articles, I wrote this article. The main topic is the study of compactness in the extension as a compact structure. they are based on a fundamental characterization of the compactness, which was given by Itai Ben Yacov and Poizat in section Basis of positive logic.