Lewis-Pye, Andrew and Barmpalias, George
(2007)
*Randomness and the linear degrees of computability.*
Annals of Pure and Applied Logic, 145 (3).
pp. 252-257.
ISSN 0168-0072

## Abstract

We show that there exists a real α such that, for all reals β, if α is linear reducible to β (α≤ℓβ, previously denoted as α≤swβ) then β≤Tα. In fact, every random real satisfies this quasi-maximality property. As a corollary we may conclude that there exists no ℓ-complete Δ2 real. Upon realizing that quasi-maximality does not characterize the random reals–there exist reals which are not random but which are of quasi-maximal ℓ-degree – it is then natural to ask whether maximality could provide such a characterization. Such hopes, however, are in vain since no real is of maximal ℓ-degree.

Item Type: | Article |
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Official URL: | http://www.journals.elsevier.com/annals-of-pure-an... |

Additional Information: | © 2006 Elsevier B.V. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 06 Aug 2013 11:13 |

Last Modified: | 20 Apr 2021 00:13 |

URI: | http://eprints.lse.ac.uk/id/eprint/51423 |

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