The Variety Generated by A(T) -- Two Counterexamples
arXiv:1304.4659 · doi:10.1007/s00012-015-0362-z
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.