2020/10/13 by Ramandi, Hossein Lamei
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2010.06125
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 ⊂ ω1, 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 ⊂ S which does not have a copy of S. This is related to a question due to Baumgartner.