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HOD, V AND THE GCH

Published online by Cambridge University Press:  21 March 2017

MOHAMMAD GOLSHANI
MOHAMMAD GOLSHANI*
Affiliation:
SCHOOL OF MATHEMATICS INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM) P.O. BOX: 19395-5746 TEHRAN, IRANE-mail: golshani.m@gmail.com
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Abstract

Starting from large cardinals we construct a model of ZFC in which the GCH fails everywhere, but such that GCH holds in its HOD. The result answers a question of Sy Friedman. Also, relative to the existence of large cardinals, we produce a model of ZFC + GCH such that GCH fails everywhere in its HOD.

Keywords

HODGCHstrong cardinalextender based Radin forcing
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 1 , March 2017 , pp. 224 - 246
Copyright
Copyright © The Association for Symbolic Logic 2017 

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References

REFERENCES

Brooke-Taylor, A. D., Large Cardinals and definable well-orders on the universe, this Journal, vol. 74 (2009), no. 2, pp. 641–654.Google Scholar
Cummings, J., David Friedman, S., and Golshani, M., Collapsing the cardinals of HOD . Journal of Mathematical Logic. vol. 15 (2015), no. 2, 32 pages.Google Scholar
Friedman, S.-D., Personal communication.Google Scholar
Friedman, S.-D. and Golshani, Mohammad, Killing GCH everywhere by a cofinality-preserving forcing notion over a model of GCH . Fundamenta Mathematicae, vol. 223 (2013), no. 2, pp. 171–193.Google Scholar
Fuchs, G., David Hamkins, J., and Reitz, J., Set-theoretic geology . Annals of Pure and Applied Logic, vol. 166 (2015), no. 4, pp. 464–501.Google Scholar
Gitik, M., Prikry-type forcings , Handbook of Set Theory, Springer, Dordrecht, 2010, pp. 1351–1447.Google Scholar
Merimovich, C., A power function with a fixed finite gap everywhere, this Journal, vol. 72 (2007), no. 2, pp. 361–417.Google Scholar
Roguski, S., The theory of the class HOD , Set Theory and Hierarchy Theory, V (Proc. Third Conf., Bierutowice, 1976), Lecture Notes in Mathematics, vol. 619, Springer, Berlin, 1977, pp. 251–255.CrossRefGoogle Scholar