Q − is a weaker variant of Robinson arithmetic Q in which addition and multiplication are partial functions, i.e. ternary relations that are graphs of possibly non-total functions. We show that Q is interpretable in Q −. This gives an alternative answer to a question of A. Grzegorczyk whether Q − is essentially undecidable.
We present a relatively simple proof, alternative to A. Visser's proof in his Growing commas article, that Robinson arithmetic is interpretable in the theory of concatenation TC.