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On the definition and the representability of quasi‐polyadic equality algebras

Miklós Ferenczi

Mathematical Logic Quarterly 62 (1-2):9-15 (2016)

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Algebraization of quantifier logics, an introductory overview.István Németi - 1991 - Studia Logica 50 (3-4):485 - 569.details This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...) Download Export citation Bookmark 43 citations
The class of infinite dimensional neat reducts of quasi‐polyadic algebras is not axiomatizable.Tarek Sayed Ahmed - 2006 - Mathematical Logic Quarterly 52 (1):106-112.details SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3]. Download Export citation Bookmark 4 citations
On Cylindric Algebras Satisfying Merry-go-round Properties.Miklós Ferenczi - 2007 - Logic Journal of the IGPL 15 (2):183-197.details Three classes are introduced which are closely related to the class included in the title. It is proven that the class obtained from by replacing axiom C4 by the commutativity of single substitutions can be considered as the abstract class in the Resek–Thompson theorem, thus it is representable by set algebras. Then the class is defined and it is shown that the necessary and sufficient condition for neat embeddability of an algebra in CAα into is the validity of the merry-go-round (...) Download Export citation Bookmark 10 citations
The class of infinite dimensional neat reducts of quasi-polyadic algebras is not axiomatizable.Tarek Ahmed - 2006 - Mathematical Logic Quarterly 52 (1):106-112.details SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3]. Download Export citation Bookmark 5 citations
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
A note on substitutions in representable cylindric algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):280-287.details We show that it is impossible to define a substitution operator for arbitrary representable cylindric algebras that agrees in its basic properties with the notion of substitutions introduced for dimension complemented algebras. Download Export citation Bookmark 2 citations

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