On Cohen and Prikry Forcing Notions
Abstract
We show that it is possible to add +-Cohen subsets to with a Prikry forcing over . This answers a question from 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 BenhamouGartieShelah. A situation with extender-based Prikry forcings is examined. This relates to a question of H. Woodin.
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