ENGLISH

Metamathematics, Machines and Gödel's Proof

By N. Shankar

Book information

Publisher
Cambridge University Press
Year
1994
ISBN
052142027X, 0511569882, 9780521585330, 9780521420273, 9780511569883, 0521585333
LCC
QA9.65 .S53 1994
Google Books ID
JmEXH9TllNcC
Language
english
Format
PDF
Filesize
2 MB (1992016 bytes)
Series
Cambridge Tracts in Theoretical Computer Science 38
Pages
218\218
Topic
Mathematics Logic
Orientation
portrait
Paginated
no
Scanned
yes
Time added
2010-05-31 15:29:46

Description

The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Gödel'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 Gödel 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.

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