Metamathematics, Machines and Gödel's Proof

ISBN-13: 9780521585330 / Angielski / Miękka / 1997 / 220 str.

Natarajan Shankar; N. Shankar; C. J. Van Rijsbergen

Opis

The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Godel'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 Godel 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.

Spis treści

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.