履歴
2018年3月19日 オンライン
2018年3月5日 JLA受理
タイトル
Randomness and Solovay degrees
(with A. Nies and F. Stephan)
種類
正論文
国際会議と雑誌
Journal of Logic and Analysis, Vol 10, pp.1–13, 2018.
Open access
Abstract
We consider the behaviour of Schnorr randomness, a randomness notion weaker than Martin-L\”of’s, for left-r.e. reals under Solovay reducibility. Contrasting with results on Martin-L\”of-randomenss, we show that Schnorr randomness is not upward closed in the Solovay degrees. Next, some left-r.e. Schnorr random $\alpha$ is the sum of two left-r.e. reals that are far from random. We also show that the left-r.e. reals of effective dimension $>r$, for some rational $r$, form a filter in the Solovay degrees.
ダウンロード