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arXiv · 2512.12446

Permutations, substitutions and finite axiomatizability

Hajnal Andréka·Zalán Gyenis·István Németi
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Abstract

Algebras of relations form an algebraic framework for the study of logical systems, extending the correspondence between Boolean algebras and propositional logic. Tarski's representable cylindric algebras $RCA_{\alpha}$, and Halmos' representable polyadic algebras $RPA_{\alpha}$ both provide algebraic counterparts to first-order logic. In this paper, we show that the usual finite set of polyadic axioms axiomatize $RPA_{\alpha}$ over $RDf_{\alpha}$, the diagonal-free subreducts of elements in $RCA_{\alpha}$. In short: $RPA_{\alpha} = PA_{\alpha} + RDf_{\alpha}$.

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Hajnal Andréka, Zalán Gyenis, István Németi. 2025-12-13. Permutations, substitutions and finite axiomatizability. https://arxiv.org/abs/2512.12446

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