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If V is a finitely generated variety such that the first-order theory of thefinite members of V is decidable, we show that V is residually finite, and infact has a finite bound on the sizes of subdirectly irreducible algebras. Thisresult generalizes known results which assumed that V has modular congruencelattices. Our proof of the theorem in its full generality proceeds by showingthat strongly solvable radicals of algebras in V are strongly abelian.

Strong solvability and residual finiteness for finitely decidable varieties