Metamathematics of First-Order Arithmetic

Metamathematics of First-Order Arithmetic

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Description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).
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Product details

  • Hardback | 474 pages
  • 162 x 240 x 36mm | 910g
  • Cambridge, United Kingdom
  • English
  • 2 Line drawings, black and white
  • 1107168414
  • 9781107168411
  • 2,818,244

Back cover copy

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 fur Mathematik und Ihre Grenzgebiete," 781.1994."
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Table of contents

Introduction; Preliminaries; Part I: 1. Arithmetic as number theory, set theory and logic; 2. Fragments and combinatorics; Part II: 3. Self-reference; 4. Models of fragments of arithmetic; Part III: 5. Bounded arithmetic; Bibliographical remarks and further reading; Bibliography; Index of terms; Index of symbols.
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Review quote

'... 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.' Roman Murawski, Mathematical Reviews '... 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 metamathematics of first-order arithmetic as well as a reference book for people working in this field.' Zentralblatt f r Mathemat k und ihre Grenzgebiete
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About Petr Hajek

Petr Hajek works in the Institute of Computer Science at the Academy of Sciences of the Czech Republic, Prague. Pavel Pudlak works in the Mathematical Institute at the Academy of Sciences of the Czech Republic, Prague.
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