Abstract
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 κ, κ + is greater than κ + of HOD. The proof uses a very general lemma showing that homogeneity is preserved through certain reverse Easton iterations.
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This work was supported by FWF grants P 16334-N05 and P 16790-N04.
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Dobrinen, N., Friedman, SD. Homogeneous iteration and measure one covering relative to HOD. Arch. Math. Logic 47, 711–718 (2008). https://doi.org/10.1007/s00153-008-0103-5
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DOI: https://doi.org/10.1007/s00153-008-0103-5