The Absorption Law, or How to Kreisel a Hilbert-Bernays-Löb

Abstract

In this paper, we show how to construct for a given consistent theory $U$ a ${\Sigma }_1^0$-predicate that both satisfies the Löb Conditions and the Kreisel Condition ---even if $U$ is unsound. We do this in such a way that $U$ itself can verify satisfaction of an internal version of the Kreisel Condition.