A MEASURABLE CARDINAL WITH A CLOSED UNBOUNDED SET OF INACCESSIBLES FROM o(κ) = κ
نویسنده
چکیده
We prove that o(κ) = κ is sufficient to construct a model V [C] in which κ is measurable and C is a closed and unbounded subset of κ containing only inaccessible cardinals of V . Gitik proved that o(κ) = κ is necessary. We also calculate the consistency strength of the existence of such a set C together with the assumption that κ is Mahlo, weakly compact, or Ramsey. In addition we consider the possibility of having the set C generate the closed unbounded ultrafilter of V while κ remains measurable, and show that Radin forcing, which requires a weak repeat point, cannot be improved on.
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