On the equational theory of representable polyadic equality algebras

Journal of Symbolic Logic 65 (3):1143-1167 (2000)
Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEA ω '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 ω 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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DOI 10.2307/2586692
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Algebraic Logic, Where Does It Stand Today?Sayed Ahmed Tarek - 2005 - Bulletin of Symbolic Logic 11 (4):465-516.
Omitting Types for Algebraizable Extensions of First Order Logic.Sayed Ahmed Tarek - 2005 - Journal of Applied Non-Classical Logics 15 (4):465-489.

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