Moreover, up to Ω-equivalence, CH is the unique Σ21-statement that is Ω-complete for Σ21; that is, letting TA be the Ω-complete theory given by ZFC + A where A is Σ21, all such TA are Ω-equivalent to TCH and hence (trivially) all such TA contain CH. In other words, there is a “good” theory and all “good” theories imply CH. 