, Volume 27, Issue 3-4, pp 348-356

Sets of degrees of computable fields

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Abstract

Given a Σ2 (resp. Σ1) degree of recursive unsolvability a, a computable field (resp. a computable field with a splitting algorithm)F is constructed in any given characteristic, such that the set of dimensions of all finite extensions ofF has degree a.

This is part of an M.Sc. Thesis presented at The Hebrew University. The author wishes to express his indebtedness to his Supervisor Professor H. Gaifman for his constant guidance and encouragement. Thanks are also due to Professor G. Sabbagh (University of Paris VII) for several useful suggestions.