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Many countable support iterations of proper forcings preserve Souslin trees

2013/09/01 by Heike Mildenberger, Saharon Shelah, Mildenberger, Heike +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #03E05 #03E17 #03E35 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Economic theories and models #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E05 #msc:03E17 #msc:03E35

paper · pdf · doi:10.48550/arxiv.1309.0196

published as Ann. Pure Appl. Logic 165 No. 2 (2014) 573--608 · 44 pages

arxiv created 2013/09/01 · openalex publication_date 2013/09/01 · arxiv updated 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation properties in countable support interations in the so-called Case A that does not need a division into forcings that add reals and those who do not.

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