A positive solution to Hilbert's 10th problem
  Polynome codes and code evaluation; arithmetical theory frames; $\mu$-recursive race for decision; decision correctness; decision termination; correct termination in theory $T = PR$ of Primitive Recursion; comparison with the negative result of Matiyasevich; positive solution in p.r. non-infinite-descent theory $\pi R=PR+(\pi).$ 
Michael Pfender
math.GM