A choice-free proof of Mal'cev's theorem on quasivarieties
Abstract
In 1966, Mal'cev proved that a class K of first-order structures with a specified signature is a quasivariety if and only if K contains a unit and is closed under isomorphisms, substructures, and reduced products. In this article, we present a proof of this theorem in ZF (the Zermelo--Fraenkel set theory without the axiom of choice).
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