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Author: Petr Hájek
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 475
ISBN-13: 1107168414
DOWNLOAD EBOOK →A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Author: Petr Hájek
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 476
ISBN-13: 1316739457
DOWNLOAD EBOOK →Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).
Author: Petr Hajek
Publisher: Springer
Published: 1998-03-17
Total Pages: 460
ISBN-13: 9783540636489
DOWNLOAD EBOOK →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.
Author: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 688
ISBN-13:
DOWNLOAD EBOOK →Author: Norman Megill
Publisher: Lulu.com
Published: 2019-06-06
Total Pages: 250
ISBN-13: 0359702236
DOWNLOAD EBOOK →Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the "Formalizing 100 Theorems" challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database.
Author: N. Shankar
Publisher: Cambridge University Press
Published: 1997-01-30
Total Pages: 224
ISBN-13: 9780521585330
DOWNLOAD EBOOK →Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author: Stephen Cole Kleene
Publisher:
Published: 2012-07-01
Total Pages: 560
ISBN-13: 9781258437961
DOWNLOAD EBOOK →Author: Raymond M. Smullyan
Publisher: Oxford University Press
Published: 1993-01-28
Total Pages: 180
ISBN-13: 0195344812
DOWNLOAD EBOOK →This work is a sequel to the author's Gödel's Incompleteness Theorems, though it can be read independently by anyone familiar with Gödel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
Author: Stephen Cole Kleene
Publisher: Courier Corporation
Published: 2013-04-22
Total Pages: 416
ISBN-13: 0486317072
DOWNLOAD EBOOK →Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
