Publication Date
3-27-2026
Document Type
Article
Organizational Units
College of Natural Science and Mathematics, Mathematics
Keywords
Relation algebras, Time warps, Graded modalities, Algebraic semantics, Substructural logics
Abstract
We prove that all varieties generated by weakening relation algebras over duals of limit ordinals have a decidable equational theory. We also show that there are only countably-many such varieties and they form a chain that embeds in. The time warp algebra is isomorphic to one of these weakening relation algebras (over the dual of the naturals), so we obtain the main result of a recent publication as a special case. The algebras we study connect to the theory of relation algebras, to time warps and graded modalities, and to the algebraic semantics of substructural logics. Our methods are inspired by the theory of lattice-ordered groups (and lattice-ordered pregroups).
Copyright Date
4-1-2026
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Rights Holder
Nikolaos Galatos and Isis A. Gallardo
Provenance
Received from Elsevier
File Format
application/pdf
Language
English (eng)
Extent
23 pgs
File Size
1.25 MB
Publication Statement
Copyright is held by the Authors. User is responsible for all copyright compliance. This article was originally published as
Galatos, N., & Gallardo, I. A. (2026). Weakening Relations Over Duals of Limit Ordinals. Journal of Pure and Applied Algebra, 230(4). https://doi.org/10.1016/j.jpaa.2026.108235
Publication Title
Journal of Pure and Applied Algebra
Volume
230
Issue
4
First Page
108235
ISSN
0022-4049
Recommended Citation
Galatos, Nikolaos and Gallardo, Isis A., "Weakening Relations Over Duals of Limit Ordinals" (2026). Mathematics: Faculty Scholarship. 62.
https://digitalcommons.du.edu/math_faculty/62
https://doi.org/10.1016/j.jpaa.2026.108235