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

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.