Weak Presentations of Computable Fields

Journal of Symbolic Logic 60 (1):199 - 208 (1995)

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Abstract
It is shown that for any computable field K and any r.e. degree a there is an r.e. set A of degree a and a field F ≅ K with underlying set A such that the field operations of F (including subtraction and division) are extendible to (total) recursive functions. Further, it is shown that if a and b are r.e. degrees with b ≤ a, there is a 1-1 recursive function $f: \mathbb{Q} \rightarrow \omega$ such that f(Q) ∈ a, f(Z) ∈ b, and the images of the field operations of Q under f can be extended to recursive functions
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DOI 10.2307/2275517
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Rational Separability Over a Global Field.Alexandra Shlapentokh - 1996 - Annals of Pure and Applied Logic 79 (1):93-108.
Weak Presentations of Non-Finitely Generated Fields.Alexandra Shlapentokh - 1998 - Annals of Pure and Applied Logic 94 (1-3):223-252.

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