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Representation Theory for Polyadic Algebras

A. Daigneault & D. Monk

Journal of Symbolic Logic 29 (3):148-148 (1964)

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Applying, extending, and specializing pseudorecursiveness.Benjamin Wells - 2004 - Annals of Pure and Applied Logic 126 (1-3):225-254.details Pseudorecursive varieties 457) exhibit a lack of recursive uniformity, expressing the failure of universal and existential quantifiers to reverse. Several examples are given of personal encounters with infeasible or errant quantifier reversal. Results strengthening and applying pseudorecursiveness are followed by the study of a property of spectra that is not uniform. These foreshadow an abstraction of this notion and its integration with the algebraic and computational studies—steps that may eventually help explicate Tarski's claim that recursively enumerable, nonrecursive but pseudorecursive equational (...) Download Export citation Bookmark
Neat embeddings as adjoint situations.Tarek Sayed-Ahmed - 2015 - Synthese 192 (7):1-37.details Looking at the operation of forming neat $\alpha $ -reducts as a functor, with $\alpha $ an infinite ordinal, we investigate when such a functor obtained by truncating $\omega $ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric (...) Download Export citation Bookmark 1 citation
Finitary Polyadic Algebras from Cylindric Algebras.Miklós Ferenczi - 2007 - Studia Logica 87 (1):1-11.details It is known that every α-dimensional quasi polyadic equality algebra (QPEA α ) can be considered as an α-dimensional cylindric algebra satisfying the merrygo- round properties . The converse of this proposition fails to be true. It is investigated in the paper how to get algebras in QPEA from algebras in CA. Instead of QPEA the class of the finitary polyadic equality algebras (FPEA) is investigated, this class is definitionally equivalent to QPEA. It is shown, among others, that from every (...) Download Export citation Bookmark 5 citations
Varying interpolation and amalgamation in polyadic MV-algebras.Tarek Sayed Ahmed - 2015 - Journal of Applied Non-Classical Logics 25 (2):140-192.details We prove several interpolation theorems for many-valued infinitary logic with quantifiers by studying expansions of MV-algebras in the spirit of polyadic and cylindric algebras. We prove for various reducts of polyadic MV-algebras of infinite dimensions that if is the free algebra in the given signature,, is in the subalgebra of generated by, is in the subalgebra of generated by and, then there exists an interpolant in the subalgebra generated by and such that. We call this a varying interpolation property because (...) Download Export citation Bookmark 1 citation
The class of polyadic algebras has the super amalgamation property.Tarek Sayed Ahmed - 2010 - Mathematical Logic Quarterly 56 (1):103-112.details We show that for infinite ordinals α the class of polyadic algebras of dimension α has the super amalgamation property. Download Export citation Bookmark 2 citations

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