Metamathematics, Machines, and Gödel's Proof
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Cambridge University Press (1994)
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.
|Keywords||Gödel's theorem Data processing Automatic theorem proving|
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|Call number||QA9.65.S53 1994|
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Citations of this work BETA
Wilfried Sieg & Clinton Field (2005). Automated Search for Gödel’s Proofs. Annals of Pure and Applied Logic 133 (1):319-338.
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