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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Grundlagen Metamathematics of First-Order Arithmetic
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Metamathematics of First-Order Arithmetic
Petr Hajek, Pavel Pudlak (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
17.03.1998
Sprache
Englisch
EAN
9783540636489
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Perspectives in Mathematical Logic
Sonderedition
Nein
Autor
Petr Hajek, Pavel Pudlak
Seitenanzahl
460
Einbandart
Broschiert
Schlagwörter
Natural, arithmetic, boundary element method, complexity, computation, computational complexity, form, incompleteness theorems, logic, mathematics, models, number theory, object, set theory, time
Thema-Inhalt
PBCD - Mathematik: Logik
PBC - Mathematische Grundlagen
UYA - Theoretische Informatik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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