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Other titles in the Pure and Applied Mathematics: A WileyInterscience Series of Texts, Monographs and Tracts series:
Logic of Mathematics: A Modern Course of Classical Logic (Pure and Applied Mathematics: A WileyInterscience Series of Texts, Monographs and Tracts)by Zofia Adamowicz
Synopses & ReviewsPublisher Comments:A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic
Logic of Mathematics combines a fullscale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * G?del's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to SkolemL?wenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logicrequiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theoryincluding a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, G?del's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as G?del's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom usethe perfect textbook for advanced students of mathematics, computer science, and logic. Book News Annotation:A mathematically rigorous presentation of basic concepts of mathematical logic, emphasizing relational structures over logical language. Part I introduces mathematical logic and model theory, with discussion of terms, formulas, and other fundamentals plus coverage of relational structures and Boolean algebras, the completeness theorem, and Peano arithmetic. Part II focuses on advanced theorems, such as Godel's theorems, the independence proof of Goodstein's theorem, and Tarski's theorem on real closed fields. Includes exercises and selected hints. For advanced students of mathematics, computer science, and logic familiar with abstract algebra.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom usethe perfect textbook for advanced students of mathematics, computer science, and logic.
Synopsis:At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logicrequiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theoryincluding a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom usethe perfect textbook for advanced students of mathematics, computer science, and logic.
Synopsis:This book looks at mathematical logic from the perspective of a mathematician rather than a logician. The authors explain the nature of mathematical reasoning and describe its applications to diverse branches of mathematics. They focus on relational structures rather than logical languages.
Description:Includes bibliographical references (p. 252256) and index.
About the AuthorZOFIA ADAMOWICZ, PhD, is a professor at the Institute of Mathematics of the Polish Academy of Sciences in Warsaw.
PAWEL ZBIERSKI, PhD, is a professor at the Department of Mathematics at Warsaw University and the coauthor of Hausdorff Gaps and Limits. Table of ContentsPartial table of contents:
MATHEMATICAL STRUCTURES AND THEIR THEORIES. Relational Systems. Boolean Algebras. Terms and Formulas. Substitution of Terms. Theorems and Proofs. Generalization Rule and Elimination of Constants. Peano Arithmetic. Ultraproducts. Supplementary Questions. SELECTED TOPICS. Total Functions. Incompleteness of Arithmetic. Tarski's Theorem. Matiyasevich's Theorem. Guide to Further Reading. References. Index. What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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