Restrictions on forcings that change cofinalities

Yair Hayut, Asaf Karagila*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper we investigate some properties of forcing which can be considered “nice” in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some “damage” to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of “nice” properties, when changing cofinalities to be uncountable.

Original languageAmerican English
Pages (from-to)373-384
Number of pages12
JournalArchive for Mathematical Logic
Issue number3-4
StatePublished - 1 May 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


  • Forcing
  • Large cardinals
  • Prikry type forcing


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