A positive solution to Hilbert's 10th problem

TL;DR

This paper presents a positive solution to Hilbert's 10th problem using primitive recursive theory, contrasting with Matiyasevich's negative result, and discusses decision correctness and termination.

Contribution

It introduces a positive resolution to Hilbert's 10th problem within primitive recursive frameworks, challenging previous negative results.

Findings

Decision correctness and termination established in primitive recursive theory

Positive solution contrasts with Matiyasevich's negative result

Framework demonstrates decision procedures in polynomial coding

Abstract

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 $\pi R=PR+(\pi).$