Abstract :
Let M/K be a finite, not completely inseparable field extension, and assume K is an infinite and recursive field. Then given any two recursively enumerable degrees image ≤ image, there exists a weak presentation j of M such that j(M) belongs to image and j(K) belongs to image. In other words, there is an isomorphism from M to a field whose universe is image so that all the field operations are total recursive functions and images of K and M belong to Turing degrees image and image respectively.
