Journal of Symbolic Logic

On the Equational Theory of Representable Polyadic Equality Algebras

Istvan Nemeti and Gabor Sagi

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Among others we will prove that the equational theory of $\omega$ dimensional representable polyadic equality algebras (RPEA$_\omega$'s) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, as well). We will also show that the complexity of the equational theory of RPEA$_\omega$ is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris [12], the following methodological conclusions will be drawn: The negative properties of polyadic (equality) algebras can be removed by switching from what we call the "polyadic algebraic paradigm" to the "cylindric algebraic paradigm".

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J. Symbolic Logic, Volume 65, Issue 3 (2000), 1143-1167.

First available in Project Euclid: 6 July 2007

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Nemeti, Istvan; Sagi, Gabor. On the Equational Theory of Representable Polyadic Equality Algebras. J. Symbolic Logic 65 (2000), no. 3, 1143--1167.

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