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Cover: 9783540636489 | Metamathematics of First-Order Arithmetic | Pavel Pudlak (u. a.)
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Metamathematics of First-Order Arithmetic
Taschenbuch von Pavel Pudlak (u. a.)
Sprache: Englisch

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Beschreibung
People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The aim of the book by Hajek and Pudlak is to cover some of the most important results in the study of a first order theory of the natural numbers, called Peano arithmetic and its fragments (subtheories). The field is quite active, but only a small part of the results has been covered in monographs. This book is divided into three parts. In Part A, the authors develop parts of mathematics and logic in various fragments. Part B is devoted to incompleteness. Part C studies systems that have the induction schema restricted to bounded formulas (Bounded Arithmetic). One highlight of this section is the relation of provability to computational complexity. The study of formal systems for arithmetic is a prerequisite for understanding results such as Gödel's theorems. This book is intended for those who want to learn more about such systems and who want to follow current research in the field. The book contains a bibliography of approximately 1000 items.
People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The aim of the book by Hajek and Pudlak is to cover some of the most important results in the study of a first order theory of the natural numbers, called Peano arithmetic and its fragments (subtheories). The field is quite active, but only a small part of the results has been covered in monographs. This book is divided into three parts. In Part A, the authors develop parts of mathematics and logic in various fragments. Part B is devoted to incompleteness. Part C studies systems that have the induction schema restricted to bounded formulas (Bounded Arithmetic). One highlight of this section is the relation of provability to computational complexity. The study of formal systems for arithmetic is a prerequisite for understanding results such as Gödel's theorems. This book is intended for those who want to learn more about such systems and who want to follow current research in the field. The book contains a bibliography of approximately 1000 items.
Zusammenfassung
This is a monograph on the metamathematics of first order arithmetic. The primary readership is active researchers and graduate students in mathematical logic, in particular those specializing in theories of the natural numbers. The middle part of the book on incompleteness may be of interest to philosophers. The last part, on computational complexity, has applications to computer science.
Inhaltsverzeichnis
Preliminaries.- A.- I: Arithmetic as Number Theory, Set Theory and Logic.- II: Fragments and Combinatorics.- B.- III: Self-Reference.- IV: Models of Fragments of Arithmetic.- C.- V: Bounded Arithmetic.- Bibliographical Remarks and Further Reading.- Index of Terms.- Index of Symbols.
Details
Erscheinungsjahr: 1998
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 476
Reihe: Perspectives in Mathematical Logic
Inhalt: xiv
460 S.
1 s/w Illustr.
460 p. 1 illus.
ISBN-13: 9783540636489
ISBN-10: 354063648X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Pudlak, Pavel
Hajek, Petr
Auflage: Softcover reprint of the original 1st ed. 1993
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Perspectives in Mathematical Logic
Maße: 235 x 155 x 26 mm
Von/Mit: Pavel Pudlak (u. a.)
Erscheinungsdatum: 17.03.1998
Gewicht: 0,715 kg
preigu-id: 106821402
Zusammenfassung
This is a monograph on the metamathematics of first order arithmetic. The primary readership is active researchers and graduate students in mathematical logic, in particular those specializing in theories of the natural numbers. The middle part of the book on incompleteness may be of interest to philosophers. The last part, on computational complexity, has applications to computer science.
Inhaltsverzeichnis
Preliminaries.- A.- I: Arithmetic as Number Theory, Set Theory and Logic.- II: Fragments and Combinatorics.- B.- III: Self-Reference.- IV: Models of Fragments of Arithmetic.- C.- V: Bounded Arithmetic.- Bibliographical Remarks and Further Reading.- Index of Terms.- Index of Symbols.
Details
Erscheinungsjahr: 1998
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 476
Reihe: Perspectives in Mathematical Logic
Inhalt: xiv
460 S.
1 s/w Illustr.
460 p. 1 illus.
ISBN-13: 9783540636489
ISBN-10: 354063648X
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Pudlak, Pavel
Hajek, Petr
Auflage: Softcover reprint of the original 1st ed. 1993
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Perspectives in Mathematical Logic
Maße: 235 x 155 x 26 mm
Von/Mit: Pavel Pudlak (u. a.)
Erscheinungsdatum: 17.03.1998
Gewicht: 0,715 kg
preigu-id: 106821402
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