Any FIP real computes a 1-generic

Abstract

We construct a computable sequence of computable reals ⟨ X i ⟩ \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. This is the first example of a classical theorem of mathematics that has been found to be equivalent, both proof theoretically and in terms of its effective content, to computing a 1-generic.