Synopses & Reviews
Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy.
An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Gödel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.
Dover (2013) republication of the edition published by PWS Publishing Company, Boston, 1995.
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Synopsis
Comprehensive overview, suitable for advanced undergraduates and graduate students, covers propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 edition.
Synopsis
This comprehensive overview of mathematical logic is designed primarily for advanced undergraduates and graduate students of mathematics. The treatment also contains much of interest to advanced students in computer science and philosophy. Topics include propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 edition.
Table of Contents
Preface 1. Background 2. Language and Semantics of Propositional Logic 3. Propositional Logic 4. First-Order Languages 5. First-Order Logic 6. Mathematics and Logic 7. Incompleteness, Undecidability and Indefinability 8. Recursive Functions 9. Compatability Theory 10. Hilbert's Tenth Problem Appendix: Number Theory References and recommended readings Index