Low upper bounds of ideals

TL;DR

The paper demonstrates the existence of a low T-upper bound for K-trivial sets, providing insights into the structure of T-degrees below 0' and their bounds in algorithmic randomness.

Contribution

It introduces a new low T-upper bound for K-trivial sets and characterizes ideals in T-degrees below 0' with such bounds.

Findings

Existence of a low T-upper bound for K-trivial sets

Characterization of ideals in T-degrees below 0' with low T-upper bounds

Extension of the result to a broader class of ideals

Abstract

We show that there is a low T-upper bound for the class of K-trivial sets, namely those which are weak from the point of view of algorithmic randomness. This result is a special case of a more general characterization of ideals in the T-degrees below 0' for which there is a low T-upper bound.