Algebraically closed structures in Positive Logic

TL;DR

This paper extends the concept of algebraically closed structures to arbitrary h-inductive theories within positive logic, exploring their properties and relationships with positive closedness and amalgamation.

Contribution

It introduces a generalized notion of positive algebraic closedness and investigates its connections with positive closedness and the amalgamation property in positive logic.

Findings

Established a generalized framework for positive algebraic closedness.

Analyzed the relationship between positive algebraic closedness and positive closedness.

Explored the implications for the amalgamation property in this context.

Abstract

In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property.