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arXiv · 1903.09882

Degree spectra for transcendence in fields

Iskander Kalimullin·Russell Miller·Hans Schoutens
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Abstract

We show that for both the unary relation of transcendence and the finitary relation of algebraic independence on a field, the degree spectra of these relations may consist of any single computably enumerable Turing degree, or of those c.e. degrees above an arbitrary fixed $\Delta^0_2$ degree. In other cases, these spectra may be characterized by the ability to enumerate an arbitrary $\Sigma^0_2$ set. This is the first proof that a computable field can fail to have a computable copy with a computable transcendence basis.

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Iskander Kalimullin, Russell Miller, Hans Schoutens. 2019-03-23. Degree spectra for transcendence in fields. https://doi.org/10.1007/978-3-030-22996-2_18

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