Positive enumerable functors

TL;DR

This paper introduces positive enumerable functors to compare structures based on enumeration reducibility, exploring their relationship with existing reduction methods in structure theory.

Contribution

It defines positive enumerable functors and analyzes their connection to established functor-based reductions and alternative approaches.

Findings

Positive enumerable functors are introduced as a new reduction method.

They relate closely to existing functor-based reductions.

The paper clarifies the role of these functors in structure comparison.

Abstract

We study reductions well suited to compare structures and classes of structures with respect to properties based on enumeration reducibility. We introduce the notion of a positive enumerable functor and study the relationship with established reductions based on functors and alternative definitions.