منابع مشابه
Uniform 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...
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 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 کاملLowness 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 کاملTitle Characterization of Kurtz Randomness by a Differentiation
Brattka, Miller and Nies [5] showed that some major algorithmic randomness notions are characterized via differentiability. The main goal of this paper is to characterize Kurtz randomness by a differentiation theorem on a computable metric space. The proof shows that integral tests play an essential part and shows that how randomness and differentiation are connected.
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2013
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/ext054