The number of clones determined by disjunctions of unary relations

Mike Behrisch; Edith Vargas-García; Dmitriy Zhuk

doi:10.1007/s00224-018-9905-y

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arXiv · 1811.11737

The number of clones determined by disjunctions of unary relations

Mike Behrisch·Edith Vargas-García·Dmitriy Zhuk

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Abstract

We consider finitary relations (also known as crosses) that are definable via finite disjunctions of unary relations, i.e. subsets, taken from a fixed finite parameter set $\Gamma$. We prove that whenever $\Gamma$ contains at least one non-empty relation distinct from the full carrier set, there is a countably infinite number of polymorphism clones determined by relations that are disjunctively definable from $\Gamma$. Finally, we extend our result to finitely related polymorphism clones and countably infinite sets $\Gamma$.

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Mike Behrisch, Edith Vargas-García, Dmitriy Zhuk. 2018-11-28. The number of clones determined by disjunctions of unary relations. https://doi.org/10.1007/s00224-018-9905-y

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