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Randomness, lowness and degrees

Barmpalias, George, Lewis-Pye, Andrew and Soskova, Mariya (2008) Randomness, lowness and degrees. Journal of Symbolic Logic, 73 (2). pp. 559-577. ISSN 0022-4812

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Identification Number: 10.2178/jsl/1208359060


We say that A≤LRB if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ, oracle B can also find patterns on γ. In other words, B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally (i.e., restricted to the computably enumerable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α is not GL2 the LR degree of α bounds 2ℵ0 degrees (so that, in particular, there exist LR degrees with uncountably many predecessors) and we give sample results which demonstrate how various techniques from the theory of the c.e. degrees can be used to prove results about the c.e. LR degrees.

Item Type: Article
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Additional Information: © 2008 Association for Symbolic Logic
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 06 Aug 2013 11:24
Last Modified: 20 May 2024 04:42

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