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A choice-free proof of Mal'cev's theorem on quasivarieties

Published 1 Jan 2025 in math.LO | (2501.00766v1)

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

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Authors (1)

  1. Guozhen Shen 

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