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Paper   IPM / M / 16082
School of Mathematics
  Title:   On Foreman's maximality principle
  Author(s):  Mohammad Golshani (Joint with Y. Hayut)
  Status:   Published
  Journal: J. Symbolic Logic
  Vol.:  81
  Year:  2016
  Pages:   1344-1356
  Supported by:  IPM
In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We prove 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 cardinals.

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