Bruno Scarpellini
(Universität Basel, Switzerland)
Undecidable Propositions by Fourier Series

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.