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Author: Petr Hájek
Publisher: Cambridge University Press
ISBN: 1107168414
Category : Mathematics
Languages : en
Pages : 475
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Book Description
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
ISBN: 1107168414
Category : Mathematics
Languages : en
Pages : 475
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Book Description
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
ISBN: 1316739457
Category : Mathematics
Languages : en
Pages : 476
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Book Description
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: Norman Megill
Publisher: Lulu.com
ISBN: 0359702236
Category : Computers
Languages : en
Pages : 250
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Book Description
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: Jan Krajicek
Publisher: Cambridge University Press
ISBN: 0521452058
Category : Computers
Languages : en
Pages : 361
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Book Description
Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688
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Book Description
Author: A. S. Troelstra
Publisher: Cambridge University Press
ISBN: 9780521779111
Category : Computers
Languages : en
Pages : 436
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Book Description
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
Author: Stephen Cole Kleene
Publisher:
ISBN: 9781258442460
Category :
Languages : en
Pages : 560
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Book Description
Author: Samuel R. Buss
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 238
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Book Description
Author: Richard Kaye
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Non-standard models of arithmetic are of interest to mathematicians through the presence of infinite integers and the various properties they inherit from the finite integers. Since their introduction in the 1930s, they have come to play an important role in model theory, and in combinatorics through independence results such as the Paris-Harrington theorem. This book is an introduction to these developments, and stresses the interplay between the first-order theory, recursion-theoretic aspects, and the structural properties of these models. Prerequisites for an understanding of the text have been kept to a minimum, these being a basic grounding in elementary model theory and a familiarity with the notions of recursive, primitive recursive, and r.e. sets. Consequently, the book is suitable for postgraduate students coming to the subject for the first time, and a number of exercises of varying degrees of difficulty will help to further the reader's understanding.
Author: Curtis Franks
Publisher: Cambridge University Press
ISBN: 0521514371
Category : Mathematics
Languages : en
Pages : 229
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Book Description
This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a different light.
