Metamathematics, Machines, and Goedel's Proof

Natarajan Shankar

Cambridge University Press, 1994

The revised Index is in:

For Table of Contents, see

Blurb: Mathematicians from Leibniz to Hilbert have sought to mechanize the verification of mathematical proofs. Developments arising out of Goedel's proof of his incompleteness theorem showed that no computer program could automatically prove all and only the valid statements of mathematics. In practice, however, there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Goedel's incompleteness theorem and the Church-Rosser theorem. 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 since metatheorems can be applied as labor-saving devices to simplify proof construction. The book should be accessible to scientists or philosophers with some knowledge of logic and computing.

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