关于劈树

Pub Date : 2023-05-28 DOI:10.1002/malq.202200022

Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle

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引用次数: 1

摘要

我们研究了分裂树强迫的两种变体，它们的理想和正则性性质。我们证明了与其他著名概念的联系，如Lebesgue可测性、Baire和Doughnut性质以及Marczewski域。此外，我们证明了任何绝对的变形虫强迫分裂树木必然会增加一个主导的实数，为Hein和Spinas关于add（I SP）≤b$\operatorname｛add｝（\mathcal{I}_\mathbb｛SP｝）\le\mathfrak｛b｝$。

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On splitting trees

We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field. Moreover, we prove that any absolute amoeba forcing for splitting trees necessarily adds a dominating real, providing more support to Hein's and Spinas' conjecture that $add (I_{SP}) \leq b$ .

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