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arXiv · 1910.08793

Entangledness in Suslin lines and trees

John Krueger
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Abstract

We introduce the idea of a weakly entangled linear order, and show that it is consistent for a Suslin line to be weakly entangled. We generalize the notion of entangled linear orders to $\omega_1$-trees, and prove that an $\omega_1$-tree is entangled iff it is free. We force the existence of a Suslin tree which is $n$-entangled, but all of whose derived trees of dimension $n+1$ are special, for any positive $n < \omega$.

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John Krueger. 2019-10-19. Entangledness in Suslin lines and trees. https://arxiv.org/abs/1910.08793

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