On Easton support iteration of Prikry type forcing notions

TL;DR

This paper explores Easton support iterations of Prikry type forcing, introducing new methods for constructing ultrafilters in extensions and revealing that diverse measures or extenders can be combined in this context.

Contribution

It presents novel techniques for ultrafilter construction in Easton support iterations of Prikry type forcing, expanding the understanding of measure interactions.

Findings

New methods for constructing normal ultrafilters in extensions

Demonstration that unrelated measures or extenders can be involved

Contrast with other support types in Prikry forcing

Abstract

We consider here Easton support iterations of Prikry type forcing notions. New ways of constructing normal ultrafilters in extensions are presented. It turns out that, in contrast with other supports, seemingly unrelated measures or extenders can be involved here.