Prikry type forcings and the Bukovsk\'y-Dehornoy phenomena

TL;DR

This paper reviews and unifies various instances of phenomena related to Prikry type forcings, highlighting their common features and extending results to several advanced forcing notions in set theory.

Contribution

It provides a coherent presentation of phenomena associated with Prikry type forcings and extends basic results to complex forcing constructions like Gitik-Shraon and Radin forcing.

Findings

Unified understanding of phenomena in Prikry type forcings

Extension of results to advanced forcing notions

Insights into the Bukovský-Dehornoy phenomena

Abstract

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 $o(\kappa) < \kappa^+$.