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

## Abstract

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 |
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Official URL: | http://link.springer.com/bookseries/558 |

Additional Information: | © 2005 Springer |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Date Deposited: | 06 Aug 2013 11:16 |

Last Modified: | 02 Jan 2024 02:06 |

URI: | http://eprints.lse.ac.uk/id/eprint/51424 |

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