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arXiv · 2402.00226

Forcing Over a Free Suslin Tree

John Krueger·Šárka Stejskalová
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Abstract

We introduce a forcing for adding almost disjoint automorphisms of a normal infinitely splitting $ω_1$-tree $T$ with countable approximations. Assuming that $T$ is a free Suslin tree, this forcing is totally proper, preserves the Suslinness of $T$, and does not add new cofinal branches of $ω_1$-trees existing in intermediate extensions. If $κ$ is an inaccessible cardinal, then the product of the automorphism forcing of length $κ$ with the Lévy collapse of $κ$ to become $ω_2$ forces that there exists an almost Kurepa Suslin tree and there does not exist a Kurepa tree. This model solves open problems due to Bilaniuk, Jin, Shelah, and Moore.

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John Krueger, Šárka Stejskalová. 2026-07-20. Forcing Over a Free Suslin Tree. https://arxiv.org/abs/2402.00226

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