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SOME APPLICATIONS OF SUPERCOMPACT EXTENDER BASED FORCINGS TO HOD

Published online by Cambridge University Press:  01 August 2018

MOTI GITIK  and
CARMI MERIMOVICH
MOTI GITIK
Affiliation:
SCHOOL OF MATHEMATICAL SCIENCES RAYMOND AND BEVERLY SACKLER FACULTY OF EXACT SCIENCES TEL AVIV UNIVERSITY RAMAT AVIV 69978, ISRAELE-mail:gitik@post.tau.ac.il
CARMI MERIMOVICH
Affiliation:
COMPUTER SCIENCE SCHOOL TEL AVIV ACADEMIC COLLEGE 2 RABENUM YEROHAM ST. TEL AVIV, ISRAELE-mail:carmi@cs.mta.ac.il
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Abstract

Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V. In particular, a model where all regular uncountable cardinals are measurable in HOD is constructed.

Keywords

Primary 03E3503E55large cardinalsextender based forcingHODEaston iteration
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 461 - 476
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

REFERENCES

Ben-Neria, O. and Unger, S., Homogenerous changes in cofinalities with applications to HOD. Journal of Mathematical Logic, vol. 17 (2017), no. 2, 1750007.CrossRefGoogle Scholar
Cummings, J., Friedman, S. D., and Golshani, M., Collapsing the cardinals of hod. Journal of Mathematical Logic, vol. 15 (2015), no. 02, pp. 1550007.CrossRefGoogle Scholar
Cummings, J., Friedman, S.-D., Magidor, M., Sinapova, D., and Rinot, A., Ordinal definable subsets of singular cardinals. Israel Journal of Mathematics, to appear.Google Scholar
Dobrinen, N. and Friedman, S.-D., Homogeneous iteration and measure one covering relative to HOD. Archive for Mathematical Logic, vol. 47 (2008), no. 7–8, pp. 711–718.CrossRefGoogle Scholar
Gitik, M. and Magidor, M., The singular cardinal hypothesis revisited, Set Theory of the Continuum (Judah, H., Just, W., and Woodin, W. H., editors), Mathematical Sciences Research Institute Publications, vol. 26, Springer, New York, 1992, pp. 243–279.CrossRefGoogle Scholar
Magidor, M., Changing the cofinality of cardinals. Fundamenta Mathematicae, vol. 99 (1978), no. 1, pp. 61–71.CrossRefGoogle Scholar
Merimovich, C., Extender-based Radin forcing. Transactions of the American Mathematical Society, vol. 355 (2003), pp. 1729–1772.CrossRefGoogle Scholar
Merimovich, C., Supercompact extender based Prikry forcing. Archive for Mathematical Logic, vol. 50 (2011), no. 5–6, pp. 592—601.CrossRefGoogle Scholar
Merimovich, C., Supercompact extender based Magidor-Radin forcing. Annals of Pure and Applied Logic, vol. 168 (2017), no. 8, pp. 1571–1587.CrossRefGoogle Scholar
Woodin, W. H., Suitable extender models I. Journal of Mathematical Logic, vol. 10 (2010), no. 1-2, pp. 101–339.CrossRefGoogle Scholar