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 prove that a variant of Robinson arithmetic Q with non-total operations is interpretable in the theory of concatenation TC introduced by A. Grzegorczyk. Since Q is known to be interpretable in that non-total variant, our result gives a positive answer to the problem whether Q is in-terpretable in TC. An immediate consequence is essential undecidability… (More)