HOD, V and the GCH
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 $HOD$.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.06192
 Bibcode:
 2015arXiv151206192G
 Keywords:

 Mathematics  Logic
 EPrint:
 arXiv admin note: text overlap with arXiv:1510.02937