Metamathematics of First-Order Arithmetic

Petr Hajek, Pavel Pudlak (Autoren)

Buch | Softcover

XIV, 460 Seiten

1998 | 1. Softcover reprint of the original 1st ed. 1993
Springer Berlin (Verlag)
978-3-540-63648-9 (ISBN)

Artikel merken

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.

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.

Erscheint lt. Verlag	17.3.1998
Reihe/Serie	Perspectives in Mathematical Logic
Zusatzinfo	XIV, 460 p. 1 illus.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	734 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
Schlagworte	arithmetic • Arithmetik • Boundary element method • Complexity • Computation • Computational Complexity • Form • HC/Mathematik/Grundlagen • Incompleteness theorems • Logic • Mathematics • Metamathematik • Models • NATURAL • Number Theory • object • set theory • Time
ISBN-10	3-540-63648-X / 354063648X
ISBN-13	978-3-540-63648-9 / 9783540636489
Zustand	Neuware