Metamathematics of First-Order Arithmetic

Name: Metamathematics of First-Order Arithmetic
Brand: Springer, Berlin
SKU: 9783540636489
Price: 561.07 PLN
Availability: InStock

Autor: Petr Hájek, Pavel Pudlak

Język:

Oprawa: Miękka

Wydawca: Springer, Berlin

Dostępność: Dostępna u dostawcy

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People have always been interested in numbers, in particular the natural numbers. Of course, we all...

Informacje o książce

Autor

Petr Hájek, Pavel Pudlak

Język

Angielski

Oprawa

Książka - Miękka

Data wydania

1998

strony

460

EAN

9783540636489

ISBN

354063648X

Enbook ID

06809734

Wydawca

Springer, Berlin

Waga

734

Wymiary

155 x 235 x 25

Pełny opis

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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