A model with Suslin trees but no minimal uncountable linear orders other than ω₁ and -ω₁

2018/03/09 by Dániel T. Soukup, Soukup, Dániel T.
Computer Science · Economics, Econometrics and Finance · Mathematics · #03E04 #03E35 #06A05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Economic theories and models #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1803.03583

openalex publication_date 2018/03/09 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

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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