# Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)

## Petr Hajek; Pavel Pudlak

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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.

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Book Description:

This much-needed monograph on the metamathematics of first-order arithmetic pays particular attention to subsystems (fragments) of Peano arithmetic and gives the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness.

From the Back Cover:

From the reviews: ..."This work is a very important contribution to the logical literature. It gives a survey of an incredible number of results and methods in the foundations of arithmetic, presented in a clear and systematic way. It will certainly be highly appreciated by specialists working in the field." Mathematical Reviews, USA 1994 ..."It is really a highly interesting book - a survey of a large amount of results presented in a systematic and clear way. It will serve as a source of information for those who want to learn meta-mathematics of first-order arithmetic as well as a reference book for people working in this field." Zentralblatt für Mathematik und Ihre Grenzgebiete, 781.1994.

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## 1.Metamathematics of First-Order Arithmetic

Editorial: Springer-Verlag Berlin and Heidelberg GmbH and Co. KG (1998)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 1998. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9783540636489

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## 2.Metamathematics of First-Order Arithmetic

Editorial: Springer (2016)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9783540636489_lsuk

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## 3.Metamathematics of First-Order Arithmetic

Editorial: Springer (1998)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer, 1998. Paperback. Estado de conservación: NEW. 9783540636489 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0421205

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## 4.Metamathematics of First-Order Arithmetic

Editorial: Springer-Verlag Berlin and Heidelberg GmbH and Co. KG (1998)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 1998. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IQ-9783540636489

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## 5.Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)

Editorial: Springer (2013)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer, 2013. Estado de conservación: New. This item is printed on demand for shipment within 3 working days. Nº de ref. de la librería LP9783540636489

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## 6.Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)

Editorial: Springer (2017)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer, 2017. Paperback. Estado de conservación: New. Never used! This item is printed on demand. Nº de ref. de la librería P11354063648X

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## 7.Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)

Editorial: Springer (2017)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer, 2017. Paperback. Estado de conservación: New. Never used! This item is printed on demand. Nº de ref. de la librería 354063648X

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## 8.Metamathematics of First-Order Arithmetic (Paperback)

Editorial: Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany (1998)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Descripción Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 1998. Paperback. Estado de conservación: New. Language: English . Brand New Book ***** Print on Demand *****.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 Godel 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. Softcover reprint of the original 1st ed. 1993. Nº de ref. de la librería AAV9783540636489

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## 9.Metamathematics of First Order Arithmetic

Editorial: Springer
ISBN 10: 354063648X ISBN 13: 9783540636489
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(Las Vegas, NV, Estados Unidos de America)
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Descripción Springer. Paperback. Estado de conservación: New. Paperback. 460 pages. Dimensions: 9.2in. x 6.1in. x 1.2in.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 Gdels 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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Nº de ref. de la librería 9783540636489

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## 10.Metamathematics of First-Order Arithmetic (Perspectives in Mathematical Logic)

Editorial: Springer (1998)
ISBN 10: 354063648X ISBN 13: 9783540636489
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Irish Booksellers
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Descripción Springer, 1998. Paperback. Estado de conservación: New. book. Nº de ref. de la librería M354063648X

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