Journal of Symbolic Logic

On the Equational Theory of Representable Polyadic Equality Algebras

Istvan Nemeti and Gabor Sagi

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Abstract

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".

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746173

Mathematical Reviews number (MathSciNet)
MR1791368

Zentralblatt MATH identifier
0964.03070

JSTOR
links.jstor.org

Citation

Nemeti, Istvan; Sagi, Gabor. On the Equational Theory of Representable Polyadic Equality Algebras. J. Symbolic Logic 65 (2000), no. 3, 1143--1167. https://projecteuclid.org/euclid.jsl/1183746173


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