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arXiv · 2611.01576

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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Patrizio Cintioli. 2026-11-01. 1-Genericity Is Not Weihrauch Reducible to the Finite Intersection Principle. https://arxiv.org/abs/2611.01576

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