$\Psi$-Spaces and Semi-Proximality
| Autor: | Almontashery, Khulod, Rodrigues, Vinicius de Oliveira, Szeptycki, Paul J. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We discuss the proximal game and semi-proximality in $\Psi$-spaces of almost disjoint families over an infinite countable set and $\Psi$-spaces of ladder systems on $\omega_1$. We show that a semi-proximal almost disjoint families must be nowhere MAD, anti-Luzin and characterize semi-proximality for a class of ${\mathbb R}$-embeddable almost disjoint families. We show that a $\Psi$-spaces defined from a uniformizable ladder system is semi-proximal and a $\Psi$-space defined on a $\clubsuit^*$ sequence is not semi-proximal. Thus the existence of non-semi-proximal $\Psi$-space over a ladder system is independent of ZFC. Comment: 18 pages |
| Databáze: | arXiv |
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