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arXiv · 2603.10539

Almost Kurepa Suslin trees and destructibility of the Guessing Model Property

Chris Lambie-Hanson·Šárka Stejskalová
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Abstract

Building on recent work of Krueger and the second author, we prove the consistency of the Guessing Model Principle at $\omega_2$ together with the existence of an almost Kurepa Suslin tree. In particular, it is consistent that the Guessing Model Principle holds but is destructible by a ccc forcing of size $\omega_1$. We also prove the consistency of the existence of a weak Kurepa tree together with the failure of the Kurepa Hypothesis and a certain guessing model principle that, for example, implies the tree property at $\omega_2$.

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Chris Lambie-Hanson, Šárka Stejskalová. 2026-03-11. Almost Kurepa Suslin trees and destructibility of the Guessing Model Property. https://arxiv.org/abs/2603.10539

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