Overview
- Provides a comprehensive introduction to universal algebraic logic
- Illustrates applications of algebraic logic with proofs of theorems and cases of study
- Can be used in the classroom for three courses in algebraic logic at different levels of difficulty
Part of the book series: Studies in Universal Logic (SUL)
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Table of contents (7 chapters)
Keywords
- Logic
- Universal ALgebra
- Tarskian Algebraic Logic
- Abstract Algebraic Logic
- Institutions
- Abstract Model Theory
- Duality Theories
- Category-Theoretic Properties of Classes of Algebras
- Surjectivity of Epimorphisms
- Amalgamation
- Interpolation
- Definability Theory
- Relation Algebra
- Cylindric Algebra
- Substitution Properties
- First Order Logic
- Sentential Logics
- Weak Beth Definability Property
- Finite Variable Fragment of First Order Logic
- First Order Logic With Nonstandard Semantics
About this book
This book gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon.
This book, apart from beinga monograph containing state of the art results in algebraic logic, can be used as the basis for a number of different courses intended for both novices and more experienced students of logic, mathematics, or philosophy. For instance, the first two chapters can be used in their own right as a crash course in Universal Algebra.
Authors and Affiliations
Bibliographic Information
Book Title: Universal Algebraic Logic
Book Subtitle: Dedicated to the Unity of Science
Authors: Hajnal Andréka, Zalán Gyenis, István Németi, Ildikó Sain
Series Title: Studies in Universal Logic
DOI: https://doi.org/10.1007/978-3-031-14887-3
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-14886-6Published: 02 November 2022
Softcover ISBN: 978-3-031-14889-7Published: 03 November 2023
eBook ISBN: 978-3-031-14887-3Published: 01 November 2022
Series ISSN: 2297-0282
Series E-ISSN: 2297-0290
Edition Number: 1
Number of Pages: XV, 327
Number of Illustrations: 1 b/w illustrations