On the rigidity of Souslin trees and their generic branches

We show it is consistent that there is a Souslin tree \(S\) such that after forcing with \(S\), \(S\) is Kurepa and for all clubs \(C \subset \omega_1\), \(S\upharpoonright C\) is rigid. This answers Fuchs's questions in Club degrees of rigidity and almost Kurepa trees. Moreover, we show it is...

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Veröffentlicht in:arXiv.org 2023-06
1. Verfasser: Ramandi, Hossein Lamei
Format: Artikel
Sprache:eng
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Zusammenfassung:We show it is consistent that there is a Souslin tree \(S\) such that after forcing with \(S\), \(S\) is Kurepa and for all clubs \(C \subset \omega_1\), \(S\upharpoonright C\) is rigid. This answers Fuchs's questions in Club degrees of rigidity and almost Kurepa trees. Moreover, we show it is consistent with \(\diamondsuit\) that for every Souslin tree there is a dense \(X \subset S\) which does not have a copy of \(S\). This is related to a question due to Baumgartner.
ISSN:2331-8422