  Let p/q be a rational number. Numeration in base p/q is defined by a function
that evaluates each finite word over A_p={0,1,...,p-1} to some rational number.
We let N_p/q denote the image of this evaluation function. In particular, N_p/q
contains all nonnegative integers and the literature on base p/q usually
focuses on the set of words that are evaluated to nonnegative integers; it is a
rather chaotic language which is not context-free. On the contrary, we study
here the subsets of (N_p/q)^d that are p/q-recognisable, i.e. realised by
finite automata over (A_p)^d. First, we give a characterisation of these sets
as those definable in a first-order logic, similar to the one given by the
B\"uchi-Bruy\`ere Theorem for integer bases numeration systems. Second, we show
that the natural order relation and the modulo-q operator are not
p/q-recognisable.
