4 Nov 2013, Published online
16 May 2013, Submitted to a Journal
Uniform Kurtz randomness
(with Takayuki Kihara)
Journal of Logic and Computation, 24 (4): 863-882, 2014
We propose studying uniform Kurtz randomness, which is the uni- form 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 characterizations, such as those via complexity, martingales, Kurtz tt-traceability, and Kurtz dimensional measure.