roseh@RATLIFF.UTEXAS.EDU (Rose M. Herring) (02/28/86)
University of Texas Computer Sciences Department COLLOQUIUM SPEAKER: N. Shankar University of Texas at Austin TITLE: Checking the Proof of Godel's Incompleteness Theorem with the Boyer-Moore Theorem Prover DATE: Thursday, March 6, 1986 PLACE: WEL 3.502 TIME: 4:00-5:30 p.m. There is a widespread belief that computer proof-checking of significant mathematics is infeasible. We argue against this by presenting a machine-checked proof of Godel's incompleteness theorem, one of the greatest landmarks of mathematics. The proof of this theorem was checked in a constructive logic with the Boyer-Moore theorem prover. The proof demonstrates the essential incompleteness of Cohen's axioms for hereditarily finite sets. This was done by first formalizing a proof-checker for this log- ic, extending it with derived inference rules, demonstrating the representability of a Lisp Eval function by a predicate in this logic, and then constructing an undecidable sentence. The state- ment of the incompleteness theorem as proved, asserts that if the undecidable sentence is either provable or disprovable, then it is both provable and disprovable. This shows that the above ax- iom system is either incomplete or inconsistent.