
Metamathematics of First-Order Arithmetic
Springer (Publisher)
Published on 17. March 1998
Book
Paperback/Softback
XIV, 460 pages
978-3-540-63648-9 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1993
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
1 s/w Abbildung
XIV, 460 p. 1 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 26 mm
Weight
715 gr
ISBN-13
978-3-540-63648-9 (9783540636489)
DOI
10.1007/978-3-662-22156-3
Schweitzer Classification
Other editions
Additional editions
Petr Hajek | Pavel Pudlak
Metamathematics of First-Order Arithmetic
Book
02/1993
Springer
€106.95
Article exhausted; check different version
Content
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.