We prove that a variant of Robinson arithmetic with nontotal operations is interpretable in the theory of concatenation introduced by A. Grzegorczyk. Since is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether is interpretable in . An immediate consequence is essential undecidability of .
"On Interpretability in the Theory of Concatenation." Notre Dame J. Formal Logic 50 (1) 87 - 95, 2009. https://doi.org/10.1215/00294527-2008-029