منابع مشابه
Lowness for Kurtz randomness
We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are ...
متن کاملLowness for uniform Kurtz randomness
We propose studying uniform Kurtz randomness, which is the uniform relativization of Kurtz randomness. One advantage of this notion is that lowness for uniform Kurtz randomness has many characterizations, such as those via complexity, martingales, Kurtz tt-traceability, and Kurtz dimensional measure.
متن کاملLowness for Demuth Randomness
We show that every real low for Demuth randomness is of hyperimmune-free degree.
متن کاملHigher Kurtz randomness
A real x is ∆1-Kurtz random (Π 1 1-Kurtz random) if it is in no closed null ∆1 set (Π 1 1 set). We show that there is a cone of Π 1 1-Kurtz random hyperdegrees. We characterize lowness for ∆1-Kurtz randomness as being ∆ 1 1-dominated and ∆ 1 1semi-traceable.
متن کاملUniform Kurtz randomness
We propose studying uniform Kurtz randomness, which is the uniform relativization of Kurtz randomness. This notion has more natural properties than the usual relativization. For instance, van Lambalgen’s theorem holds for uniform Kurtz randomness while not for (the usual relativization of) Kurtz randomness. Another advantage is that lowness for uniform Kurtz randomness has many characterization...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2009
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1243948333