Working with the LR degrees

Authors:
George Barmpalias;Andrew E. M. Lewis;Mariya Soskova
Affiliations:
School of Mathematics, University of Leeds, Leeds, UK;Dipartimento di Scienze Matematiche ed Informatiche, Via del Capitano, Siena;School of Mathematics, University of Leeds, Leeds, UK
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Recursively enumerable sets and degrees

Recursively enumerable sets and degrees
Visualization 2001 Conference (Acm

Visualization 2001 Conference (Acm
A Cappable Almost Everywhere Dominating Computably Enumerable Degree

Electronic Notes in Theoretical Computer Science (ENTCS)
Computability and Randomness

Computability and Randomness

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Abstract

We say that A ≤LR B 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 propose a methodology for studying the LR degrees and present a number of recent results of ours, including sketches of their proofs.