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arXiv · 2204.02860

On Cohen and Prikry Forcing Notions

Tom Benhamou·Moti Gitik
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Abstract

We show that it is possible to add $κ^+-$Cohen subsets to $κ$ with a Prikry forcing over $κ$. 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.

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Tom Benhamou, Moti Gitik. 2022-10-18. On Cohen and Prikry Forcing Notions. https://doi.org/10.1017/jsl.2023.59

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