Source: J. Symbolic Logic
Volume 73, Issue 2
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.
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