An Interpretation of Robinson Arithmetic in its Grzegorczyk's Weaker Variant
Vítězslav Švejdar · Fundamenta Informaticae · 2008
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.