Relations between some theories of semigroups (also known as theories of strings or theories of concatenation) and arithmetic are surveyed. In particular Robinson's arithmetic Q is shown to be mutually interpretable with TC, a weak theory of concatenation introduced by Grzegorczyk. Furthermore, TC is shown to be interpretable in the theory F studied by Tarski and Szmielewa, thus confirming their claim that F is essentially undecidable.
"Arithmetic on semigroups." J. Symbolic Logic 74 (1) 265 - 278, March 2009. https://doi.org/10.2178/jsl/1231082312