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On the equational theory of representable polyadic equality algebras

Published online by Cambridge University Press:  12 March 2014

István Németi  and
Gábor Sági
István Németi
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest PF. 127, H-1364, Hungary E-mail: [email protected]
Gábor Sági
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest PF. 127, H-1364, Hungary E-mail: [email protected]
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Abstract

Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEAω'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 RPEAω is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildikó 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”.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 1143 - 1167
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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