On Roitman's principles $\mathsf{MH}$ and $\Delta$
| Autor: | Barriga-Acosta, Hector, Brian, Will, Dow, Alan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Model Hypothesis (abbreviated $\mathsf{MH}$) and $\Delta$ are set-theoretic axioms introduced by J. Roitman in her work on the box product problem. Answering some questions of Roitman and Williams on these two principles, we show (1) $\mathsf{MH}$ implies the existence of $P$-points in $\omega^*$ and is therefore not a theorem of $\mathsf{ZFC}$; (2) $\mathsf{MH}$ also fails in the side-by-side Sacks models; (3) as $\Delta$ holds in these models, this implies $\Delta$ is strictly stronger than $\mathsf{MH}$; (4) furthermore, $\Delta$ holds in a large class of forcing extensions in which it was not previously known to hold. Comment: 18 pages, 1 diagram |
| Databáze: | arXiv |
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