• G. Fuchs and J. D. Hamkins, “The Bukovský-Dehornoy phenomenon for Boolean ultrapowers,” ArXiv e-prints, 2017.
  [Bibtex]

  @ARTICLE{FuchsHamkins:TheBukovskyDehornoyPhenomenonForBooleanUltrapowers,
  AUTHOR = {Gunter Fuchs and Joel David Hamkins},
  TITLE = {The {Bukovsk\'y-Dehornoy} phenomenon for {Boolean} ultrapowers},
  JOURNAL = {ArXiv e-prints},
  YEAR = {2017},
  volume = {},
  number = {},
  pages = {},
  month = {},
  note = {Under review},
  abstract = {},
  keywords = {under-review},
  source = {},
  eprint = {1707.06702},
  archivePrefix = {arXiv},
  primaryClass = {math.LO},
  url = {http://wp.me/p5M0LV-1zz},
  }

Abstract. We show that while the length $\omega$ iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Příkrý forcing, it is consistent that no iteration of length greater than $\omega$ (of the same ultrafilter and its images) is a Boolean ultrapower. For longer iterations, where different ultrafilters are used, this is possible, though, and we give Magidor forcing and a generalization of Příkrý forcing as examples. We refer to the discovery that the intersection of the finite iterates of the universe by a normal measure is the same as the generic extension of the direct limit model by the critical sequence as the Bukovský-Dehornoy phenomenon, and we develop a criterion (the existence of a simple skeleton) for when a version of this phenomenon holds in the context of Boolean ultrapowers.