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...

We introduce and develop a topological semantics of conservativity logics interpretability logics. prove the compactness theorem consistent normal extensions logic $\mathbf{CL}$ by extending Shehtman's ultrabouquet construction method to our framework. As consequence, we that several such as $\mathbf{IL}$, $\mathbf{ILM}$, $\mathbf{ILP}$ $\mathbf{ILW}$ are strongly complete with respect semantics.