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Paper   IPM / M / 16072
School of Mathematics
  Title:   HOD, V and the GCH
  Author(s):  Mohammad Golshani
  Status:   Published
  Journal: J. Symbolic Logic
  Year:  2017
  Pages:   224-246
  Supported by:  IPM
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.

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