Introduction To Metamathematics
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Introduction To Metamathematics
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Author : Stephen Cole Kleene
language : en
Publisher:
Release Date : 1971
Introduction To Metamathematics written by Stephen Cole Kleene and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Functions categories.
Introduction To Metamathematics
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Author : S.C. Kleene
language : en
Publisher: North Holland
Release Date : 1980-01-01
Introduction To Metamathematics written by S.C. Kleene and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Computers categories.
Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gadel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which nothing was ever the same. Kleene was an important figure in logic, and lived a long full life of scholarship and teaching. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gade1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Gadel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.
Mathematical Logic
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Author : Stephen Cole Kleene
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Mathematical Logic written by Stephen Cole Kleene and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
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.
Introduction To Metamathematics
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Author : Stephen Cole Kleene
language : en
Publisher:
Release Date : 1952
Introduction To Metamathematics written by Stephen Cole Kleene and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1952 with Mathematics categories.
Metamathematics Machines And G Del S Proof
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Author : N. Shankar
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-30
Metamathematics Machines And G Del S Proof written by N. Shankar and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-30 with Computers categories.
Describes the use of computer programs to check several proofs in the foundations of mathematics.
An Introduction To Ramsey Theory
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Author : Matthew Katz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03
An Introduction To Ramsey Theory written by Matthew Katz and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamathematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey's theorem for graphs and hypergraphs, van der Waerden's theorem on arithmetic progressions, infinite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
Logic Semantics Metamathematics
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Author : Alfred Tarski
language : en
Publisher: Hackett Publishing
Release Date : 1983-01-01
Logic Semantics Metamathematics written by Alfred Tarski and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Philosophy categories.
Introduction To Logic
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Author : Alfred Tarski
language : en
Publisher: Courier Corporation
Release Date : 2013-07-04
Introduction To Logic written by Alfred Tarski and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-04 with Mathematics categories.
This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
Metamath A Computer Language For Mathematical Proofs
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Author : Norman Megill
language : en
Publisher: Lulu.com
Release Date : 2019
Metamath A Computer Language For Mathematical Proofs written by Norman Megill and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Computers categories.
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.
Recursion Theory For Metamathematics
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Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press
Release Date : 1993-01-28
Recursion Theory For Metamathematics written by Raymond M. Smullyan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-28 with Mathematics categories.
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.