Fast-collapsing theories

Abstract

Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.

14 pages, 1 figure. Amendment to correct bibliography

References in corpus (1)

• A machine that knows its own code

Cited by in corpus (1)

• Strengthening Consistency Results in Modal Logic