English

Left computably enumerable reals and initial segment complexity

Logic in Computer Science 2022-08-02 v1

Abstract

We are interested in the computability between left c.e. reals α\alpha and their initial segments. We show that the quantity C(C(αn)αn)C(C(\alpha_n)|\alpha_n) plays a crucial role in this and in their completeness. We look in particular at Chaitin's theorem and its relativisation due to Frank Stephan.

Cite

@article{arxiv.2208.00423,
  title  = {Left computably enumerable reals and initial segment complexity},
  author = {George Davie},
  journal= {arXiv preprint arXiv:2208.00423},
  year   = {2022}
}

Comments

13 pages

R2 v1 2026-06-25T01:21:37.057Z