A model with Suslin trees but no minimal uncountable linear orders other than $\omega_1$ and $-\omega_1$

Dániel T. Soukup

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arXiv · 1803.03583

A model with Suslin trees but no minimal uncountable linear orders other than $\omega_1$ and $-\omega_1$

Dániel T. Soukup

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Abstract

We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than $\omega_1$ and $-\omega_1$, answering a question of J. Baumgartner. This is done by a Jensen-type iteration, proving that one can force CH together with a restricted form of ladder system uniformization on trees, all while preserving a rigid Suslin tree.

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BibTeX RIS

Dániel T. Soukup. 2018-03-09. A model with Suslin trees but no minimal uncountable linear orders other than $\omega_1$ and $-\omega_1$. https://arxiv.org/abs/1803.03583

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