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arXiv · 1304.4659

The Variety Generated by A(T) -- Two Counterexamples

Matthew Moore
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Abstract

We show that V(A(T)) does not have definable principal subcongruences or bounded Maltsev depth. When the Turing machine T halts, V(A(T)) is an example of a finitely generated semilattice based (and hence congruence meet-semidistributive) variety with only finitely many subdirectly irreducible members, all finite. This is the only known example of a variety with these properties that does not have definable principal subcongruences or bounded Maltsev depth.

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Matthew Moore. 2013-04-17. The Variety Generated by A(T) -- Two Counterexamples. https://doi.org/10.1007/s00012-015-0362-z

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