Metamathematics, Machines and Godel's Proof by Natarajan Shankar (English) Paper

Description: Metamathematics, Machines and Godel's Proof by Natarajan Shankar The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Godel's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of Godel and Church-Rosser. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning, because metatheorems can be applied as labor-saving devices to simplify proof construction. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Godels first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of Godel and Church-Rosser. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning, because metatheorems can be applied as labor-saving devices to simplify proof construction. Table of Contents 1. Introduction; 2. The statement of the incompleteness theorem; 3. Derived inference rules; 4. The representability of metatheory; 5. The undecidable sentence; 6. A mechanical proof of the Church-Rosser theorem; 7. Conclusions. Promotional "Headline" Describes the use of computer programs to check several proofs in the foundations of mathematics. Description for Bookstore Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including G Description for Library Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including G Details ISBN0521585333 Author Natarajan Shankar Pages 220 Publisher Cambridge University Press Language English ISBN-10 0521585333 ISBN-13 9780521585330 Media Book Format Paperback DEWEY 511.3 Series Number 0038 Year 1997 Publication Date 1997-01-31 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Series Cambridge Tracts in Theoretical Computer Science (Paperback) Short Title METAMATHEMATICS MACHINES & GOD Edition Description Revised Illustrations 4 Line drawings, unspecified DOI 10.1604/9780521585330 Audience Professional and Scholarly UK Release Date 1997-01-30 AU Release Date 1997-01-30 NZ Release Date 1997-01-30 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:91374219;

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