On a question of sacks: a partial solution on the positive side
Lewis-Pye, A.
(2005).
On a question of sacks: a partial solution on the positive side.
In
Cooper, S. B., Löwe, B. & Torenvliet, L.
(Eds.),
New Computational Paradigms: First Conference on Computability in Europe, Cie 2005, Amsterdam, the Netherlands, June 8-12, 2005
(pp. 275-286).
Springer Berlin / Heidelberg.
https://doi.org/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 | Chapter |
|---|---|
| Copyright holders | © 2005 Springer |
| Departments | LSE > Academic Departments > Mathematics |
| DOI | 10.1007/11494645_34 |
| Date Deposited | 06 Aug 2013 |
| URI | https://researchonline.lse.ac.uk/id/eprint/51424 |
Explore Further
- https://www.scopus.com/pages/publications/26444497996 (Scopus publication)
- http://link.springer.com/bookseries/558 (Official URL)