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PreprintarXiv licencearXiv

1-Genericity Is Not Weihrauch Reducible to the Finite Intersection Principle

  • Patrizio Cintioli
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Abstract

This paper shows that the problem of producing a Cohen $1$-generic real relative to a given oracle is not Weihrauch reducible to the finite intersection principle (FIP). More strongly, no nontrivial computable FIP instance admits a single Turing functional that produces an absolute $1$-generic real from every enumeration of every maximal centered set of indices. The argument combines a $1$-generic real that computes no perfect tree all of whose paths are $1$-generic with local constancy and a parametrization of maximal centered sets. This answers Question~9.10.25 of Dzhafarov and Mummert.

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Cite

BibTeXRIS
BibTeX
@misc{cintioli20261genericity,
  title = {{1-Genericity Is Not Weihrauch Reducible to the Finite Intersection Principle}},
  author = {Patrizio Cintioli},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01576},
  eprint = {2611.01576},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01576},
}
RIS
TY  - UNPB
TI  - 1-Genericity Is Not Weihrauch Reducible to the Finite Intersection Principle
AU  - Patrizio Cintioli
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01576
UR  - https://arxiv.org/abs/2611.01576
AB  - This paper shows that the problem of producing a Cohen $1$-generic real relative to a given oracle is not Weihrauch reducible to the finite intersection principle (FIP). More strongly, no nontrivial computable FIP instance admits a single Turing functional that produces an absolute $1$-generic real from every enumeration of every maximal centered set of indices. The argument combines a $1$-generic real that computes no perfect tree all of whose paths are $1$-generic with local constancy and a parametrization of maximal centered sets. This answers Question~9.10.25 of Dzhafarov and Mummert.
ER  -