"The very strong conjectures are to be confirmed by complementary analysis that will begin tomorrow morning," Mackowiak said.
In fact, arguments provided in [15, 28] allow to prove stronger conjecture (C^*(1/2)) for these classes of groups.
We discuss a stronger conjecture about the structure of the automorphism group Aut RT,ST), and a weaker one about entropy as a conjugacy invariant.
Note that there exist much stronger conjectured bounds (see [ 16, Conjecture 1.4.4] and [ 18, Conjecture 27]).
(This lemma is named strong perfect conjecture in some studies).
We now prove the strong convergence conjecture (II).
Moreover, (again, assuming the Strong Ω Conjecture) there is a maximal such theory and in that theory 2ℵ0 = ℵ2.
where here AD+ is a strengthening of AD. (Strong Ω conjecture) Assume there is a proper class of Woodin cardinals.
Moreover, in the maximal theory T given by the size of the continuum is ℵ2.[9] To summarize: Assuming the Strong Ω Conjecture, there is a "good" theory of H ω2) and all such theories imply that CH fails.
Though the strong openness conjecture deserves a more elaborate treatment, we have to make some hard choices of things to leave out, lest this article continue to grow unboundedly.
