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arXiv · 2101.01594

Specializing Trees with Small Approximations I

Rahman Mohammadpour
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Abstract

Assuming $\rm PFA$, we shall use internally club $\omega_1$-guessing models as side conditions to show that for every tree $T$ of height $\omega_2$ without cofinal branches, there is a proper and $\aleph_2$-preserving forcing notion with finite conditions which specialises $T$. Moreover, the forcing has the $\omega_1$-approximation property.

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Rahman Mohammadpour. 2021-01-05. Specializing Trees with Small Approximations I. https://arxiv.org/abs/2101.01594

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