NONSTANDARD EXTENSIONS OF WEAK PRESENTATIONS

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 a less than or equal to b, there exists a weak presentation j of M such that j(M) belongs to b and j(K) belongs to a. In other words, there is an isomorphism from M to a field whose universe is N so that all the field operations are total recursive functions and images of K and M belong to Turing degrees a and b respectively. (C) 1995 Academic Press, Inc.