Metamathematics, machines, and Gödel's proof
著者
書誌事項
Metamathematics, machines, and Gödel's proof
（Cambridge tracts in theoretical computer science, 38）
Cambridge University Press, 1994
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Goedel'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 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 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.
目次
- 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.
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