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arXiv · 2004.10840

On splitting trees

Giorgio Laguzzi·Heike Mildenberger·Brendan Stuber-Rousselle
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Abstract

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 \emph{absolute} amoeba forcing for splitting trees necessarily adds a dominating real, providing more support to Spinas' and Hein's conjecture that $\add(\ideal{I}_\spl) \leq \mathfrak{b}$.

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Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle. 2020-04-22. On splitting trees. https://arxiv.org/abs/2004.10840

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