 There is also a parallel with the second step. Recall that for the second step in the previous subsection we had that although the various TA did not agree, they all contained ¬CH and, moreover, from among them there is one that stands out, namely the theory given by (∗), since this theory maximizes the Π2-theory of the structure ⟨H(ω2), ∈, INS,  A | A ∈ P (ℝ) ∩ L(ℝ)⟩. In the present context of CH we again (assuming the conjecture) have that although the TA do not agree, they all contain CH. It turns out that once again, from among them there is one that stands out, namely, the maximum one. For it is known (by a result of Woodin in 1985) that if there is a proper class of measurable Woodin cardinals then there is a forcing extension satisfying all Σ22 sentences φ such that ZFC + CH + φ is Ω-satisfiable (see Ketchersid, Larson, &amp; Zapletal (2010)).  It follows that if the question of existence is answered positively with an A that is Σ22 then TA must be this maximum Σ22 theory and, consequently, all TA agree when A is Σ22. So, assuming that there is a TA where A is Σ22, then, although not all TA agree (when A is arbitrary) there is one that stands out, namely, the one that is maximum for Σ22 sentences. 