Weak presentations of non-finitely generated fields

Annals of Pure and Applied Logic 94 (1-3):223-252 (1998)
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Abstract

Let K be a countable field. Then a weak presentation of K is an isomorphism of K onto a field whose elements are natural numbers, such that all the field operations are extendible to total recursive functions. Given a pair of two non-finitely generated countable fields contained in some overfield, we investigate under what circumstances the overfield has a weak presentation under which the given fields have images of arbitrary Turing degrees or, in other words, we investigate Turing separability of various pairs of non-finitely generated fields

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Citations of this work

Generalized weak presentations.Alexandra Shlapentokh - 2002 - Journal of Symbolic Logic 67 (2):787-819.

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References found in this work

Weak Presentations of Computable Fields.Carl G. Jockusch & Alexandra Shlapentokh - 1995 - Journal of Symbolic Logic 60 (1):199 - 208.
Diophantine equivalence and countable rings.Alexandra Shlapentokh - 1994 - Journal of Symbolic Logic 59 (3):1068-1095.
Rational separability over a global field.Alexandra Shlapentokh - 1996 - Annals of Pure and Applied Logic 79 (1):93-108.

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