This paper develops the philosophy and technology needed for adding a supremum operator to the interpretability logic ILM of Peano Arithmetic (PA). It is wellknown that any theories extending PA have a supremum in the interpretability ordering. While provable in PA, this fact is not reflected in the theorems of the modal system ILM, due to limited expressive power. Our goal is to enrich the lan...

Abstract Kristiansen and Murwanashyaka recently proved that Robinson arithmetic, Q, is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T Q by producing a formal interpretation concatenation QT + , thereby also establishing mutual interpretability with several well-known weak essentially undecidable theories numbers, strings, sets. introduce “hybrid” str...