User blog comment:Wythagoras/FGH of Array Notations/@comment-1605058-20130705193651

I don't know if you really understand what inaccessible cardinal is - it isn't limit of Omega_Omega_Omega_... In fact, inaccessible ordinals are so large, that their existence is unprovable in ZFC, as they imply consistency of ZFC. They are pretty complicated thing when it comes to collapsing functions.