Saturation of the closed unbounded filter on the set of regular cardinals

Jech, Thomas J.; Woodin, W. Hugh

doi:10.1090/S0002-9947-1985-0805967-1

Saturation of the closed unbounded filter on the set of regular cardinals
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by Thomas J. Jech and W. Hugh Woodin PDF

Trans. Amer. Math. Soc. 292 (1985), 345-356 Request permission

Abstract:

For any $\alpha < {\kappa ^ + }$, the following are equiconsistent: (a) $\kappa$ is measurable of order $\alpha$, (b) $\kappa$ is $\alpha$-Mahlo and the filter ${\mathbf {C}}[\operatorname {Reg} ]$ is saturated.

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