Logic of Mathematics: A Modern Course of Classical Logic (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) - Hardcover

Adamowicz, Zofia; Zbierski, Pawel

 
9780471060260: Logic of Mathematics: A Modern Course of Classical Logic (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
Hardcover
ISBN 10: 0471060267 ISBN 13: 9780471060260
Verlag: Wiley-Interscience, 1997

Inhaltsangabe

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 full-scale 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:
* Gödel'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 Skolem-Löwenheim 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 logic-requiring 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 theory-including 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 use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Über die Autorin bzw. den Autor

ZOFIA 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.

Von der hinteren Coverseite

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 full-scale 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:
* Gödel'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 Skolem-Löwenheim 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 logic-requiring 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 theory-including 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 use-the perfect textbook for advanced students of mathematics, computer science, and logic.

Aus dem Klappentext

At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring 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 theory-including 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 use-the perfect textbook for advanced students of mathematics, computer science, and logic.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Wiley-Interscience
Erscheinungsdatum
1997
Sprache
Englisch
ISBN 10 
0471060267
ISBN 13 
9780471060260
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
272
Kontakt zum Hersteller
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