 where recall that H(κ+) is the collection of sets of hereditary cardinality less than κ+. Thus, assuming ZFC and that there is a proper class of Woodin cardinals, the set  𝒱Ω is Turing equivalent to the set of Π2 generic multiverse truths and the set  𝒱Ω(H(κ+)) is precisely the set of generic multiverse truths of H(κ+). 