On Foreman’s maximality principle

Mohammad Golshani, Yair Hayut

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 collapses some cardinal.

Original languageAmerican English
Pages (from-to)1344-1356
Number of pages13
JournalJournal of Symbolic Logic
Issue number4
StatePublished - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2016, Association for Symbolic Logic.


  • Adding reals
  • Collapsing cardinals
  • Extender based Radin forcing
  • Extender sequences


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