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On a question of sacks: a partial solution on the positive side

Lewis-Pye, Andrew (2005) On a question of sacks: a partial solution on the positive side. In: Cooper, S. Barry, Löwe, Benedikt and Torenvliet, Leen, (eds.) New Computational Paradigms: First Conference on Computability in Europe, Cie 2005, Amsterdam, the Netherlands, June 8-12, 2005. Lecture notes in computer science (3526). Springer Berlin / Heidelberg, Berlin, pp. 275-286. ISBN 9783540261797

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Identification Number: 10.1007/11494645_34


Let us say that a c.e. operator E is degree invariant on any given Turing degree a if X,Y ∈ a → E(X) ≡  T E(Y) . In [4] we construct a c.e. operator E such that ∀X [ X <  T E(X) <  T X′] . While we are unable to produce degree invariance everywhere, we are able to ensure that for every degree a there exists b such that a ∨ 0′ = b ∨ 0′ and E is degree invariant on b . What appears here is an abbreviated version of the material from that paper, stopping short of most technical details.

Item Type: Book Section
Official URL:
Additional Information: © 2005 Springer
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 06 Aug 2013 11:16
Last Modified: 16 May 2024 05:01

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