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Some combinatorial properties of splitting trees

Volume 70 / 2022

Jonathan Schilhan 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


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.


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