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PreprintCC BY 4.0arXiv

Escaping and generics over ideals

  • Laurent Bienvenu
  • Noam Greenberg
  • Ludovic Patey
  • Dan Turetsky
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Abstract

We study the relation between the existence of escaping (or hyperimmune) functions and weak 1-genericity using computability over ideals. We prove in particular the existence of an ℐ-escaping function which does not ℐ-compute any weakly ℐ-generic set whenever ℐ is a countable Turing ideal closed under the existence of diagonally non-computable functions.

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Cite

BibTeXRIS
BibTeX
@misc{bienvenu2026escaping,
  title = {{Escaping and generics over ideals}},
  author = {Laurent Bienvenu and Noam Greenberg and Ludovic Patey and Dan Turetsky},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06439},
  eprint = {2611.06439},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06439},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Escaping and generics over ideals
AU  - Laurent Bienvenu
AU  - Noam Greenberg
AU  - Ludovic Patey
AU  - Dan Turetsky
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06439
UR  - https://arxiv.org/abs/2611.06439
AB  - We study the relation between the existence of escaping (or hyperimmune) functions and weak 1-genericity using computability over ideals. We prove in particular the existence of an ℐ-escaping function which does not ℐ-compute any weakly ℐ-generic set whenever ℐ is a countable Turing ideal closed under the existence of diagonally non-computable functions.
ER  -