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  1. Home
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  3. Metamathematics, Machines and Gödel's Proof
  • Cited by 38
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
1994
Online ISBN:
9780511569883
DOI:
https://doi.org/10.1017/CBO9780511569883
Subjects:
Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Programming Languages and Applied Logic
Series:
Cambridge Tracts in Theoretical Computer Science (38)
Information

Book description

Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Gödel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice, however, there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Gödel'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 mechanisation of metamathematics itself has important implications for automated reasoning since metatheorems can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists and philosophers with some knowledge of logic and computing.

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