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Metamathematics, machines, and Godel's proof / N. Shankar

By: Series: Cambridge tracts in theoretical computer science ; 38Publication details: Cambridge, U.K. : Cambridge University Press, 1997Description: xv, 202 p. ; 25 cmISBN:
  • 0521585333
Subject(s): DDC classification:
  • 511.3028553 SHA
Contents:
1. Introduction. - 2. The Statement of the Incompleteness Theorem. - 3. Derived Inference Rules. - 4. The Representability of the Metatheory. - 5. The Undecidable Sentence. - 6. A Mechanical Proof of the Church-Rosser Theorem. - 7. Conclusions. - Bibliography.
Summary: ...This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Godel'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 theorms. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning since metatheorms can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists or philosophers with some knowledge of logic and computing. - Back cover
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1. Introduction. - 2. The Statement of the Incompleteness Theorem. - 3. Derived Inference Rules. - 4. The Representability of the Metatheory. - 5. The Undecidable Sentence. - 6. A Mechanical Proof of the Church-Rosser Theorem. - 7. Conclusions. - Bibliography.

...This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Godel'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 theorms. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning since metatheorms can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists or philosophers with some knowledge of logic and computing. - Back cover