Any FIP real computes a 1-generic

TL;DR

The paper constructs computable sequences of reals to show that any real computing a maximal finite intersection property subsequence can also compute a Cohen 1-generic, extending to 2IP cases.

Contribution

It demonstrates that any real computing a FIP or 2IP maximal subsequence can also compute a Cohen 1-generic, establishing a new connection between these concepts.

Findings

Any real computing a FIP maximal subsequence can compute a Cohen 1-generic.

Extension of the result to 2IP cases.

Provides a new link between computability and genericity.

Abstract

We construct a computable sequence of computable reals $\langle X_i\rangle$ such that any real that can compute a subsequence that is maximal with respect to the finite intersection property can also compute a Cohen 1-generic. This is extended to establish the same result with 2IP in place of FIP.