## Lowness Properties and Randomness

by
André Nies

Venue: | ADVANCES IN MATHEMATICS |

Citations: | 78 - 21 self |

### BibTeX

@INPROCEEDINGS{Nies_lownessproperties,

author = {André Nies},

title = {Lowness Properties and Randomness},

booktitle = {ADVANCES IN MATHEMATICS},

year = {},

pages = {274--305},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

The set A is low for Martin-Lof random if each random set is already random relative to A. A is K-trivial if the prefix complexity K of each initial segment of A is minimal, namely K(n)+O(1). We show that these classes coincide. This implies answers to questions of Ambos-Spies and Kucera [2], showing that each low for Martin-Lof random set is # 2 . Our class induces a natural intermediate # 3 ideal in the r.e. Turing degrees (which generates the whole class under downward closure). Answering