Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s 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.
Author(s): Hajnal Andréka, Miklós Ferenczi, István Németi (auth.), Hajnal Andréka, Miklós Ferenczi, István Németi (eds.)
Series: Bolyai Society Mathematical Studies 22
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2013
Language: English
Pages: 466
Tags: Mathematical Logic and Foundations; Algebra; Combinatorics; Mathematical Logic and Formal Languages
Front Matter....Pages 1-7
Introduction....Pages 9-12
Front Matter....Pages 13-13
Reducing First-order Logic to Df 3 , Free Algebras....Pages 15-35
Varieties of Two-Dimensional Cylindric Algebras....Pages 37-59
Completions and Complete Representations....Pages 61-89
Amalgamation, Interpolation and Epimorphisms in Algebraic Logic....Pages 91-103
Neat Reducts and Neat Embeddings in Cylindric Algebras....Pages 105-131
Front Matter....Pages 133-133
A New Representation Theory: Representing Cylindric-like Algebras by Relativized Set Algebras....Pages 135-162
Representing all Cylindric Algebras by Twisting on a Problem of Henkin....Pages 163-182
Front Matter....Pages 183-183
Representable Cylindric Algebras and Many-Dimensional Modal Logics....Pages 185-203
Completions, Complete Representations and Omitting Types....Pages 205-221
Elements of Cylindric Algebraic Model Theory....Pages 223-248
Cylindric Modal Logic....Pages 249-269
Front Matter....Pages 271-271
Crs and Guarded Logics: A Fruitful Contact....Pages 273-301
Cylindric Probability Algebras....Pages 303-320
Cylindric Algebras and Relational Databases....Pages 321-331
Probability Measures and Measurable Functions on Cylindric Algebras....Pages 333-347
Front Matter....Pages 349-349
Cylindric Set Algebras and IF Logic....Pages 351-366
Polyadic Algebras....Pages 367-389
Front Matter....Pages 391-391
Definability Issues in Universal Logic....Pages 393-419
Back Matter....Pages 421-478
