## Journal of Symbolic Logic

### On the Equational Theory of Representable Polyadic Equality Algebras

#### 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

https://projecteuclid.org/euclid.jsl/1183746173

Mathematical Reviews number (MathSciNet)
MR1791368

Zentralblatt MATH identifier
0964.03070

JSTOR