Randomness below complete theories of arithmetic
Logic
2022-11-17 v3
Abstract
We show that degrees containing a complete extensions of arithmetic have the random join property: they are the supremum of any random real they compute, with another random real. The same is true for the truth-table and weak truth-table reducibilities.
Cite
@article{arxiv.2206.04996,
title = {Randomness below complete theories of arithmetic},
author = {George Barmpalias and Wei Wang},
journal= {arXiv preprint arXiv:2206.04996},
year = {2022}
}