Abstract
Harrington extended the first half of Rabin’s Theorem to differential fields, proving that every computable differential field can be viewed as a computably enumerable subfield of a computable presentation of its differential closure. For fields F, the second half of Rabin’s Theorem says that this subfield is Turing-equivalent to the set of irreducible polynomials in F[X]. We investigate possible extensions of this second half, asking both about the degree of the differential field K within its differential closure and about the degree of the set of constraints for K, which forms the closest analogue to the set of irreducible polynomials.
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Miller, R., Ovchinnikov, A. (2011). Adapting Rabin’s Theorem for Differential Fields. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_22
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DOI: https://doi.org/10.1007/978-3-642-21875-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21874-3
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