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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

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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 

References

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