2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74152We discuss a rational version of a conjecture of Matiyasevich, Davis, and Putnam on the relative decidability of the finiteness problem for Diophantine equations with respect to the existence problem. We formulate a suspicion that for rational solutions, the finiteness problem should be relatively decidable in contrast to the M-D-P conjecture for integer solutions.Lecture at the mid-west model theory meeting, December, 2004Number TheoryLogic11D99text