Metamathematics, Machines and Gödel's Proof

by N. Shankar

Overview

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.

Product Details

ISBN-13:	9780521585330
Publisher:	Cambridge University Press
Publication date:	01/30/1997
Series:	Cambridge Tracts in Theoretical Computer Science , #38
Edition description:	REPRINT
Pages:	220
Product dimensions:	6.89(w) x 9.76(h) x 0.67(d)

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.