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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 $\omega_1$-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 $\omega_1$-trees existing in intermediate extensions. If $\kappa$ is an inaccessible cardinal, then the product of the automorphism forcing of length $\kappa$ with the L\'{e}vy collapse of $\kappa$ to become $\omega_2$ 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. 2024-01-31. Forcing Over a Free Suslin Tree. https://arxiv.org/abs/2402.00226

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