### Randomness and Solovay degrees

#### Abstract

We consider the behaviour of Schnorr randomness, a randomness notion weaker than Martin-Löf's, for left-r.e. reals under Solovay reducibility. Contrasting with results on Martin-Löf-randomenss, we show that Schnorr randomness is not upward closed in the Solovay degrees. Next, some left-r.e. Schnorr random

*α*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.#### Full Text:

3. [PDF]DOI: https://doi.org/10.4115/jla.2018.10.3

This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Logic and Analysis ISSN: 1759-9008