arXiv subjects

Matthew Smedberg

Publications and source records attributed to Matthew Smedberg.

2 recordsLinked to original sources

arXiv2013

Strong solvability and residual finiteness for finitely decidable varieties

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.

math.LO↗

arXiv2013

Bounding essential arities of term operations in finitely decidable varieties

Let $\mathbf{A}$ be a finite algebra generating a finitely decidable variety and having nontrivial strongly solvable radical $τ$. We provide an improved bound on the number of variables in which a term can be sensitive to changes within $τ$. We utilize a multi-sorted algebraic construction, amalgamating the methods developed by Valeriote and McKenzie for the investigation of strongly abelian locally finite decidable varieties with those of Idziak for locally finite congruence modular finitely decidable varieties.

math.LO↗