# Uniform Kurtz randomness

2013年11月4日　オンライン
2013年5月16日　投稿

タイトル
Uniform Kurtz randomness
(with Takayuki Kihara)

Journal of Logic and Computation, 24 (4): 863-882, 2014
doi: 10.1093/logcom/ext054

アブストラクト
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.

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