Abstract
We show that the existence of a Suslin tree does not necessarily imply that there are uncountable minimal linear orders other than ω1 and −ω1, 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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Soukup, D.T. A model with Suslin trees but no minimal uncountable linear orders other than ω1 and −ω1. Isr. J. Math. 233, 199–224 (2019). https://doi.org/10.1007/s11856-019-1899-x
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DOI: https://doi.org/10.1007/s11856-019-1899-x