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Title Cylindric-like algebras and algebraic logic / Hajnal Andreka, Miklos Ferenczi, Istvan Nemeti (eds.)
Published Berlin : Springer : JBMS, Janos Bolyai Mathematical Society, 2013
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Description 1 online resource (478 pages) : illustrations
Series Bolyai society mathematical studies, 1217-4696 ;; 22
Bolyai Society mathematical studies ;; 22
Contents Introduction -- H. Andrka and I. Nmeti: Reducing First-order Logic to Df3, Free Algebras -- N. Bezhanishvili: Varieties of Two-Dimensional Cylindric Algebras -- R. Hirsch and I. Hodkinson: Completions and Complete Representations -- J. Madarsz and T. Sayed Ahmed: Amalgamation, Interpolation and Epimorphisms in Algebraic Logic -- T. Sayed Ahmed: Neat Reducts and Neat Embeddings in Cylindric Algebras -- M. Ferenczi: A New Representation Theory: Representing Cylindric-like Algebras by Relativized Set Algebras -- A. Simon: Representing all Cylindric Algebras by Twisting, On a Problem of Henkin -- A. Kurucz: Representable Cylindric Algebras and Many-Dimensional Modal Logics -- T. Sayed Ahmed: Completions, Complete Representations and Omitting Types -- G. Serny: Elements of Cylindric Algebraic Model Theory -- Y. Venema: Cylindric Modal Logic -- J. van Benthem: Crs and Guarded Logics: A Fruitful Contact -- R.S. Dordevic and M.D. Raskovic: Cylindric Probability Algebras.-I. Duentsch: Cylindric Algebras and Relational Databases. M. Ferenczi: Probability Measures and Measurable Functions on Cylindric Algebras. A. Mann: Cylindric Set Algebras and IF Logic. G. Sgi: Polyadic Algebras. I. Sain: Definability Issues in Universal Logic
Summary Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarskis quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (cylindric in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin
Bibliography Includes bibliographical references and indexes
Notes Print version record
Subject Cylindric algebras.
Algebraic logic.
Mathematical Concepts.
Form Electronic book
Author Andréka, H., editor
Ferenczi, M. (Miklós), 1947- editor
Németi, I., editor
ISBN 3642350259 (electronic bk.)
9783642350252 (electronic bk.)
(Springer ;;) (hd. bd.)
(Janos Bolyai Mathematical Society ;;) (hd. bd.)