The complexity of classifying continuous t-norms up to isomorphism

Jialiang He; Lili Shen; Yi Zhou

doi:10.1016/j.topol.2025.109684

The complexity of classifying continuous t-norms up to isomorphism

Jialiang He
, Lili Shen
, Yi Zhou

Sichuan University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	109684
Journal	Topology and its Applications
Volume	378
DOIs	https://doi.org/10.1016/j.topol.2025.109684
State	Published - 1 Feb 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 Elsevier B.V.

Keywords

Borel complete equivalence relation
Borel reducibility
Complexity of equivalence relations
Isomorphism of continuous t-norms

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10.1016/j.topol.2025.109684

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AU - Shen, Lili

AU - Zhou, Yi

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AB - 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.

KW - Borel complete equivalence relation

KW - Borel reducibility

KW - Complexity of equivalence relations

KW - Isomorphism of continuous t-norms

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The complexity of classifying continuous t-norms up to isomorphism

Abstract

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Keywords

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