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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brooke-Taylor, A., Friedman, S.-D.: Large cardinals and morasses (to appear)
Cummings, J.: Iterated forcing and elementary embeddings. In: Foreman, M., Kanamori, A., Magidor, M. (eds.) Handbook of Set Theory. Kluwer, Dordrecht (to appear)
Dobrinen N., Friedman S.-D.: Internal consistency and global co-stationarity of the ground model. J. Symbolic Logic 73(2), 512–521 (2008)
Friedman, S.-D.: Large cardinals and L-like universes. In: Set theory: recent trends and applications, Quaderni di Matematica, vol. 17, pp. 93–110. Dept. Math., Seconda Univ. Napoli, Caserta (2006)
Jech T.: Set Theory, the 3rd millennium edn. Springer, Berlin (2003)
Kanamori A.: The Higher Infinite, 2nd edn. Springer, Berlin (2003)
Kunen K.: Set Theory, an Introduction to Independence Proofs. North-Holland, Amsterdam (1980)
Steel, J.R.: The core model iterability problem. In: Lecture Notes in Logic, vol. 8. Springer, Berlin (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by FWF grants P 16334-N05 and P 16790-N04.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-008-0103-5