Journal of Symbolic Logic 73 (2):559 - 577 (2008)
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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. 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 enumberable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α in not GL₂ the LR degree of α bounds $2^{\aleph _{0}}$ 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
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DOI | 10.2178/jsl/1208359060 |
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References found in this work BETA
Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Citations of this work BETA
Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Mass Problems and Hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
Π 1 0 Classes, L R Degrees and Turing Degrees.George Barmpalias, Andrew E. M. Lewis & Frank Stephan - 2008 - Annals of Pure and Applied Logic 156 (1):21-38.
The K -Degrees, Low for K Degrees,and Weakly Low for K Sets.Joseph S. Miller - 2009 - Notre Dame Journal of Formal Logic 50 (4):381-391.
Relative Randomness and Cardinality.George Barmpalias - 2010 - Notre Dame Journal of Formal Logic 51 (2):195-205.
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