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2 results

  • HOD, V AND THE GCH

  • MOHAMMAD GOLSHANI
  • Journal:
    The Journal of Symbolic Logic / Volume 82 / Issue 1 / March 2017
    Published online by Cambridge University Press:
    21 March 2017, pp. 224-246
    Print publication:
    March 2017

  • 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.

  • ON FOREMAN’S MAXIMALITY PRINCIPLE

  • MOHAMMAD GOLSHANI, YAIR HAYUT
  • Journal:
    The Journal of Symbolic Logic / Volume 81 / Issue 4 / December 2016
    Published online by Cambridge University Press:
    29 September 2016, pp. 1344-1356
    Print publication:
    December 2016

  • In this paper, we consider Foreman’s maximality principle, which says that any nontrivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We observe that it is consistent that every c.c.c. forcing adds a real and that for every uncountable regular cardinal κ, every κ-closed forcing of size 2<κ collapses some cardinal.