MUTUAL INTERPRETABILITY OF WEAK ESSENTIALLY UNDECIDABLE THEORIES

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” strings WQT*, establish its Robinson’s arithmetic R, the trees WT Murwanashyaka, WTC ε Higuchi Horihata.