Abstract
We show that \({\mathcal {V}(\mathbb {A}(\mathcal {T}))}\) does not have definable principal subcongruences or bounded Maltsev depth. When the Turing machine \({\mathcal {T}}\) halts, \({\mathcal {V}(\mathbb {A}(\mathcal {T}))}\) is an example of a finitely generated semilattice based (and hence congruence \({\wedge}\)-semidistributive) variety with only finitely many subdirectly irreducible members, all finite. This is the first known example of a variety with these properties that does not have definable principal subcongruences or bounded Maltsev depth.
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Presented by M. Maroti.
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Moore, M. The variety generated by \({\mathbb {A}(\mathcal {T})}\)– two counterexamples. Algebra Univers. 75, 21–31 (2016). https://doi.org/10.1007/s00012-015-0362-z
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DOI: https://doi.org/10.1007/s00012-015-0362-z