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arXiv · 2506.12458

Substitutions of variables are finitely axiomatizable over quantifications and permutations

Hajnal Andréka·Zalán Gyenis·István Németi
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Abstract

This paper proves that the equational theory of the class $RA_{\alpha}^{csp}$ of representable polyadic algebras is finitely axiomatizable over its substitution-free reduct $RA_{\alpha}^{cp}$, for finite $\alpha$. That is, substitutions of variables in finite variable first-order logic can be described by finitely many axioms over the Boolean operations, existential quantifiers and permutations of variables.

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Hajnal Andréka, Zalán Gyenis, István Németi. 2025-06-14. Substitutions of variables are finitely axiomatizable over quantifications and permutations. https://arxiv.org/abs/2506.12458

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