In the attempt to find structures in analysisB with non-recursive properties one is led in a natural way
to Fourier analysis which due to its proximity to algebra makes it possible to simulate logical
structures by Fourier series.
Our procedure is to start with a set B of simple periodic functions and then to generate new ones
by finitely many applications taken from a list R of elementary rules plus a strong rule ODR
which permits the construction of new functions by solving a system of algebraic ODE's.
It turns out that every diophantine predicate can be described by a periodic function generated
from B by repeated applications of the rules R and ODR.
The connection with analogue computation and a conjecture of J. R. Büchi is discussed.