Overview
- Provides a comprehensive, self-contained introduction to decidability of first-order theories, using detailed proofs and examples to illustrate and clarify complex concepts
- Incorporates computability theory and reduction techniques to determine the decidability of theories
- Illustrates a variety of ways to deduce logical consequences from a theory, including the use of Gentzen calculus for first-order logic
Part of the book series: Studies in Universal Logic (SUL)
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Table of contents (5 chapters)
Keywords
About this book
After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory.
The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field.
Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination.
Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Decidability of Logical Theories and Their Combination
Authors: João Rasga, Cristina Sernadas
Series Title: Studies in Universal Logic
DOI: https://doi.org/10.1007/978-3-030-56554-1
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-56553-4Published: 21 October 2020
Softcover ISBN: 978-3-030-56556-5Published: 22 October 2021
eBook ISBN: 978-3-030-56554-1Published: 20 October 2020
Series ISSN: 2297-0282
Series E-ISSN: 2297-0290
Edition Number: 1
Number of Pages: XIII, 178
Number of Illustrations: 69 b/w illustrations, 1 illustrations in colour
Topics: Mathematical Logic and Foundations, Mathematical Logic and Formal Languages, Philosophy of Mathematics