On Cohen and Prikry Forcing Notions
Logic
2024-05-22 v3
Abstract
We show that it is possible to add Cohen subsets to with a Prikry forcing over . This answers a question from \cite{HayutBenhanouGitik}. A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author \cite{BenhamouGartieShelah}. A situation with extender-based Prikry forcings is examined. This relates to a question of H. Woodin.
Keywords
Cite
@article{arxiv.2204.02860,
title = {On Cohen and Prikry Forcing Notions},
author = {Tom Benhamou and Moti Gitik},
journal= {arXiv preprint arXiv:2204.02860},
year = {2024}
}
Comments
Corrected typos, added details to the proof of the main theorems, and improved the result about the Merimovich Extender-based Prikry forcing: we now prove that in its general form, it cannot answer Woodin's question