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PreprintCC BY 4.0arXiv

A Note on Lowness for Π01-Immunity

  • David J. Webb
Open at sourcePDFDOICite

Abstract

We show that the only degree which cannot co-enumerate a non-trivial Π01-immune real is ∅, resolving a conjecture of the author. The main ingredient is that if a real A has that all A-maximal sets are c.e., then A has c.e. degree, which can be proved via a coding mechanism and two classical results of Lachlan.

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Cite

BibTeXRIS
BibTeX
@misc{webb2026note,
  title = {{A Note on Lowness for $Π^0_1$-Immunity}},
  author = {David J. Webb},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13297},
  eprint = {2609.13297},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13297},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Note on Lowness for Π^0_1-Immunity
AU  - David J. Webb
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.13297
UR  - https://arxiv.org/abs/2609.13297
AB  - We show that the only degree which cannot co-enumerate a non-trivial Π^0_1-immune real is ∅, resolving a conjecture of the author. The main ingredient is that if a real A has that all A-maximal sets are c.e., then A has c.e. degree, which can be proved via a coding mechanism and two classical results of Lachlan.
ER  -