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The number of normal measures. (English) Zbl 1183.03042
Without much ado, the authors state and prove their first main result: If GCH holds, $$\kappa$$ is measurable and $$\alpha$$ is a cardinal not larger than $$\kappa^{++}$$ then there is a cofinality-preserving forcing extension in which $$\kappa$$ carries exactly $$\alpha$$ normal measures. A coding trick applied to generalized Sacks forcing enables the authors to create the desired number of normal ultrafilters.
Similar results are obtained together with the failure of GCH at $$\kappa^+$$ or $$\kappa$$, e.g., one can have $$2^\kappa=\kappa^{++}$$ and exactly $$\alpha$$ many measures on $$\kappa$$ for any prescribed $$\alpha\leq\kappa^{++}$$.
Reviewer: K. P. Hart (Delft)

##### MSC:
 3e+55 Large cardinals 3e+35 Consistency and independence results 3e+50 Continuum hypothesis and Martin’s axiom
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##### References:
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