Abstract

In [6] Albert Visser shows that ILP completely axiomatizes all schemata about provability and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called $\text{ILP}^{\omega}$ that completely axiomatizes the arithmetically valid principles of provability in and interpretability over such theories. To prove the arithmetical completeness of $\text{ILP}^{\omega}$ we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result