When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?

Juan Climent Vidal, Enric Cosme Llópez

For a set of sorts $S$ and an $S$-sorted signature $\Sigma$ we prove that a profinite $\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\Sigma$-algebras, is a retract o…