 This Σ2-statement is invariant under set forcing and hence is one adherents to the generic multiverse view of truth must deem determinate. Moreover, the key arguments above go through with this Σ2-statement instead of the Ω Conjecture. The person taking this second line of response would thus also have to maintain that this statement is false. But there is substantial evidence that this statement is true. The reason is that there is no known example of a Σ2-statement that is invariant under set forcing relative to large cardinal axioms and which cannot be settled by large cardinal axioms. (Such a statement would be a candidate for an absolutely undecidable statement.) So it is reasonable to expect that this statement is resolved by large cardinal axioms. However, recent advances in inner model theory—in particular, those in Woodin (2010)—provide evidence that no large cardinal axiom can refute this statement. Putting everything together: It is very likely that this statement is in fact true ; so this line of response is not promising. 