The complexity of classifying continuous t-norms up to isomorphism

TL;DR

This paper demonstrates that classifying continuous t-norms up to isomorphism is as complex as classifying linear orders, establishing it as a Borel complete equivalence relation.

Contribution

It proves that the isomorphism relation for continuous t-norms is Borel complete, linking it to the complexity of linear order classification.

Findings

Isomorphism of continuous t-norms is Borel bireducible with linear order isomorphism.

Classification complexity of continuous t-norms matches that of linear orders.

Establishes the Borel completeness of the equivalence relation for continuous t-norms.

Abstract

It is shown that the isomorphism relation between continuous t-norms is Borel bireducible with the relation of order isomorphism between linear orders on the set of natural numbers, and therefore, it is a Borel complete equivalence relation.