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Homogeneous iteration and measure one covering relative to HOD. (English) Zbl 1153.03034

Summary: Relative to a hyperstrong cardinal, it is consistent that measure one covering fails relative to HOD. In fact it is consistent that there is a superstrong cardinal and for every regular cardinal \(\kappa\), \(\kappa ^{+}\) is greater than \(\kappa ^{+}\) of HOD. The proof uses a very general lemma showing that homogeneity is preserved through certain reverse Easton iterations.

MSC:

03E35 Consistency and independence results
03E40 Other aspects of forcing and Boolean-valued models
03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
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