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arXiv · 1609.03722

On the local closure of clones on countable sets

Erhard Aichinger
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Abstract

We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable, then there is a function $f : \mathbb{N} \to \mathbb{N}$ such that the $n$-ary part of $C$ is equal to the $n$-ary part of $\mathrm{Pol}\,\mathrm{Inv}^{[f(n)]} C$, where $\mathrm{Inv}^{[f(n)]} C$ denotes the set of $f(n)$-ary invariant relations of $C$.

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Erhard Aichinger. 2016-09-13. On the local closure of clones on countable sets. https://doi.org/10.1007/s00012-017-0465-9

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