Some combinatorial properties of splitting trees
Volume 70 / 2022
Bulletin Polish Acad. Sci. Math. 70 (2022), 1-12
MSC: Primary 03E05; Secondary 03E02, 03E17.
DOI: 10.4064/ba210622-2-6
Published online: 20 June 2022
Abstract
We show that splitting forcing does not have the weak Sacks property below any condition, answering a question of Laguzzi, Mildenberger and Stuber-Rousselle. We also show how some partition results for splitting trees hold or fail and we determine the value of cardinal invariants after an $\omega _2$-length countable support iteration of splitting forcing.
