# Why is Robinson arithmetic “Q”?

I see Peano arithmetic so often abbreviated as "P" or "PA". Why is Robinson Arithmetic "Q"? Following the obvious pattern, I would have expected R" or "RA".

I think that there is no special reason here.

See Alfred Tarski & Andrzej Mostowski & Raphael Robinson, Undecidable Theories (North Holland, 1971); Ch.2 : Undecidability in Arithmetic (page 51) deals with the :

formalized arithmetic of natural numbers [...] referred to as Theory $$\mathsf N$$.

We shall be interested in some axiomatic subtheories of $$\mathsf N$$ referred to as Theories $$\mathsf P, \mathsf Q, \mathsf R$$.

A finitely axiomatizable and essentially undecidable subtheory $$\overline {\mathsf Q}$$ of the arithmetic of natural numbers was first constructed by Mostowski and Tarski in 1939. [...] R.M.Robinson has shown that Theory $$\overline {\mathsf Q}$$ can be replaced by a weaker theory based upon a simpler axiom system, in fact, by Theory $$\mathsf Q$$.