David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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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 , 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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Citations of this work BETA
Sayed Ahmed Tarek (2005). Algebraic Logic, Where Does It Stand Today? Bulletin of Symbolic Logic 11 (4):465-516.
Hajnal Andréka (1997). Complexity of Equations Valid in Algebras of Relations Part I: Strong Non-Finitizability. Annals of Pure and Applied Logic 89 (2):149-209.
Tarek Sayed-Ahmed (2013). Neat Embeddings as Adjoint Situations. Synthese 192 (7):1-37.
Sayed Ahmed Tarek (2005). Omitting Types for Algebraizable Extensions of First Order Logic. Journal of Applied Non-Classical Logics 15 (4):465-489.
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