  This paper is meant to present in a coherent way several instances of quite
common phenomena that was first identified (independently) by Bukovsk\'y and
Dehornoy. We present the basic result for Prikry type forcing and show how to
extend it to the Gitik-Shraon forcing, the Extender Based Prikry forcing,
Prikry forcings with interleaved collapses and Radin forcing for $o(\kappa) <
\kappa^+$.
