Metamathematics of First-Order Arithmetic
Published on 22. March 2017
978-1-316-73173-4 (ISBN)
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).
Reviews / Votes
'... 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 GrenzgebieteMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
2 Line drawings, black and white
File size
41,34 MB
ISBN-13
978-1-316-73173-4 (9781316731734)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Petr Hajek | Pavel Pudlak
Metamathematics of First-Order Arithmetic
Book
03/2017
Cambridge University Press
€196.90
Shipment within 15-20 days
Persons
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.
Content
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.
