2013/11/12 by McKenzie, Ralph, Smedberg, Matthew
#03D35 #08B26 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1311.2683
If V is a finitely generated variety such that the first-order theory of the finite members of V is decidable, we show that V is residually finite, and in fact has a finite bound on the sizes of subdirectly irreducible algebras. This result generalizes known results which assumed that V has modular congruence lattices. Our proof of the theorem in its full generality proceeds by showing that strongly solvable radicals of algebras in V are strongly abelian.