9783540636489 - Metamathematics of First-Order Arithmetic di Hajek, Petr (14 risultati)

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Condizione: New. pp. 476.

Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 476 pp. Englisch.

Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. * Coverage of incompleteness of interest to philosophers concerned with its implications * Coverage of computational complexity and its connections to provability will interest computer scientistsCoverage of incompleteness of interest to philosophers.

Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This is a monograph on the metamathematics of first order arithmetic. The primary readership is active researchers and graduate students in mathematical logic, in particular those specializing in theories of the natural numbers. The middle part of the book on incompleteness may be of interest to philosophers. The last part, on computational complexity, has applications to computer science.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 476 pp. Englisch.

Condizione: New. Print on Demand pp. 476 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam.

Condizione: New. PRINT ON DEMAND pp. 476.