Randomness and reducibility

摘要

We study reducibilities that act as measures of relative randomness on reals, concentrating particularly on their behavior on the computably enumerable reals. One such reducibility, called domination or Solovay reducibility, has already proved to be a powerful tool in the study of randomness of effectively presented reals. Motivated by certain shortcomings of Solovay reducibility, we introduce two new measures of relative randomness and investigate their properties and the relationships between them and Solovay reducibility.