On functors enumerating structures

TL;DR

This paper introduces enumerable functors as a new way to relate structures, showing their equivalence to effective interpretability with computable equivalence relations, and explores their relation to computable functors.

Contribution

It establishes the equivalence between enumerable functors and effective interpretability with computable equivalence relations, advancing the understanding of structure reductions.

Findings

Enumerable functors are equivalent to effective interpretability with computable equivalence relations.

Results clarify the relationship between enumerable and computable functors.

Provides a new perspective on reductions between structures in computable model theory.

Abstract

We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the equivalence relation computable are equivalent. We also obtain results on the relation between enumerable and computable functors.