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I. Németi, G. Sági

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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 is not schema axiomatizable.
This result is in 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, too). We will also show that the complexity of the
equational theory of the class of omega dimensional representable polyadic
equality algebras is also extremely high in the recursion theoretic sense.
Finally, comparing our negative results with the positive ones of Ildiko Sain
and Viktor Gyuris, we will draw the following methodological conclusions.
The negative properties of polyadic (equality) algebras can be removed by
switching from the so called "polyadic algebraic paradigm" to the
"cylindric algebraic" one.

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