Abstract
We prove that a varietyV which is locally finite, finitely generated, congruence permutable and of finite type, and whose subdirectly irreducible algebras are all either abelian or linear type 3 above the monolith is finitely decidable if and only if the theory of the finite abelian algebras inV is decidable.
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Albert, M.H. A sufficient condition for finite decidability. Algebra Universalis 36, 467–482 (1996). https://doi.org/10.1007/BF01233917
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DOI: https://doi.org/10.1007/BF01233917