| Autor: |
Kalimullin, Iskander, Miller, Russell, Schoutens, Hans |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
Computing with Foresight and Industry: 15th Conference on Computability in Europe, CiE 2019, eds. F. Manea, B. Martin, D. Paulusma, & G. Primiero, Lecture Notes in Computer Science 11558 (Berlin: Springer-Verlag, 2019), 205--216 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/978-3-030-22996-2_18 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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