Article

Israel Journal of Mathematics

, Volume 27, Issue 3, pp 348-356

First online:

Sets of degrees of computable fields

  • Elie BienenstockAffiliated withThe Hebrew University of Jerusalem

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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.