Robinson arithmetic

Summary

Robinson arithmetic, often written $\mathsf{Q}$, is a first-order theory of the natural numbers with zero, successor, addition and multiplication. It has seven axioms and no induction. It is much weaker than the Peano axioms, yet strong enough to represent every computable function. For this reason the incompleteness theorems and many undecidability results already hold for $\mathsf{Q}$ and every consistent theory that extends it.