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 Σ01-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.