On splitting trees

Abstract

AbstractWe 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 .