A Mathematical Introduction to Logic
By- Herbert Enderton, University of California, Los Angeles, U.S.A.
A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.
Audience
Computer scientists, philosophers, mathematicians, and the educated layperson who want to learn how to apply logic.
Hardbound, 317 Pages
Published: December 2000
Imprint: Academic Press
ISBN: 978-0-12-238452-3
Reviews
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"Rigor, integrity and coherence of overall purpose, introducing students to the practice of logic . . ."
Reasons for This Book's Success , --Douglas Cannon, University of Washington
"The book is clearly and carefully written. I adopted this text because of its detailed and rigorous treatment of the predicate calculus, detailed and optimal treatment of the incompleteness phenomena, standard notation as developed by the Berkeley school."
--Karel Prikry, University of Minnesota
"It is mathematically rigorous [and] it has more examples than other books . . . I definitely would use a new edition of this book."
--Sun-Joo Chin, University of Notre Dame
Contents
- USEFUL FACTS ABOUT SETSSENTENTIAL LOGIC * Informal Remarks on Formal Languages * The Language of Sentential Logic * Induction and Recursion * Truth Assignments * Unique Readability * Sentential Connectives * Switching Circuits * Compactness and EffectivenessFIRST-ORDER LOGIC Preliminary Remarks * First-Order Languages * Truth and Models * Unique Readability * A Deductive Calculus * Soundness and Completeness Theorems * Models of Theories * Interpretations between Theories * Nonstandard AnalysisUNDECIDABILITY Number Theory * Natural Numbers with Successor * Other Reducts of Number Theory * A Subtheory of Number Theory * Arithmetization of Syntax * Incompleteness and Undecidability * Applications to Set Theory * Representing Exponentiation * Recursive FunctionsSECOND-ORDER LOGIC Second-Order Languages * Skolem Functions * Many-Sorted LogicGeneral Structures
