Transactions of the American Mathematical Society

A measurable cardinal with a closed unbounded set of inaccessibles from $o(\kappa)=\kappa$

Author(s): William Mitchell
Journal: Trans. Amer. Math. Soc. 353 (2001), 4863-4897.
MSC (2000): Primary 03E35, 03E45, 03E55
Posted: July 17, 2001
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We prove that $o(\kappa)=\kappa$ is sufficient to construct a model

in which $\kappa$ is measurable and

is a closed and unbounded subset of $\kappa$ containing only inaccessible cardinals of

. Gitik proved that $o(\kappa)=\kappa$ is necessary.

We also calculate the consistency strength of the existence of such a set

together with the assumption that $\kappa$ is Mahlo, weakly compact, or Ramsey. In addition we consider the possibility of having the set

generate the closed unbounded ultrafilter of

while $\kappa$ remains measurable, and show that Radin forcing, which requires a weak repeat point, cannot be improved on.

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William Mitchell
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: mitchell@math.ufl.edu

DOI: 10.1090/S0002-9947-01-02853-7
PII: S 0002-9947(01)02853-7
Received by editor(s): March 30, 2001
Posted: July 17, 2001
Additional Notes: This work was partially supported by grant number DMS-962-6143 from the National Science Foundation.
Copyright of article: Copyright 2001, American Mathematical Society

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