A choice-free proof of Mal'cev's theorem on quasivarieties
arXiv:2501.00766 · doi:10.1007/s00012-025-00902-x
Abstract
In 1966, Mal'cev proved that a class of first-order structures with a specified signature is a quasivariety if and only if contains a unit and is closed under isomorphisms, substructures, and reduced products. In this article, we present a proof of this theorem in (the Zermelo--Fraenkel set theory without the axiom of choice).
5 pages