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Author: Petr Hájek
Publisher: Cambridge University Press
Published: 2017-03-02
Total Pages: 475
ISBN-13: 1107168414
DOWNLOAD EBOOKA 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 EBOOKSince 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
Published: 2019
Total Pages: 250
ISBN-13: 0359702236
DOWNLOAD EBOOKMetamath 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: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 688
ISBN-13:
DOWNLOAD EBOOKAuthor: Stephen Cole Kleene
Publisher:
Published: 2012-07-01
Total Pages: 560
ISBN-13: 9781258442460
DOWNLOAD EBOOKAuthor: Stephen Cole Kleene
Publisher: Courier Corporation
Published: 2013-04-22
Total Pages: 436
ISBN-13: 0486317072
DOWNLOAD EBOOKContents 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.
Author: Jan Krajicek
Publisher: Cambridge University Press
Published: 1995-11-24
Total Pages: 361
ISBN-13: 0521452058
DOWNLOAD EBOOKDiscusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.
Author: A. S. Troelstra
Publisher: Cambridge University Press
Published: 2000-07-27
Total Pages: 436
ISBN-13: 9780521779111
DOWNLOAD EBOOKThis 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: Akihiro Kanamori
Publisher: Springer Science & Business Media
Published: 2008-11-23
Total Pages: 555
ISBN-13: 3540888675
DOWNLOAD EBOOKOver the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.
Author: Richard Kaye
Publisher:
Published: 1991
Total Pages: 312
ISBN-13:
DOWNLOAD EBOOKNon-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.
