Club degrees of rigidity and almost Kurepa trees

Archive for Mathematical Logic 52 (1-2):47-66 (2013)
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Abstract

A highly rigid Souslin tree T is constructed such that forcing with T turns T into a Kurepa tree. Club versions of previously known degrees of rigidity are introduced, as follows: for a rigidity property P, a tree T is said to have property P on clubs if for every club set C (containing 0), the restriction of T to levels in C has property P. The relationships between these rigidity properties for Souslin trees are investigated, and some open questions are stated.

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Citations of this work

On the rigidity of Souslin trees and their generic branches.Hossein Lamei Ramandi - 2022 - Archive for Mathematical Logic 62 (3):419-426.

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References found in this work

Degrees of rigidity for Souslin trees.Gunter Fuchs & Joel David Hamkins - 2009 - Journal of Symbolic Logic 74 (2):423-454.
Can a small forcing create Kurepa trees.Renling Jin & Saharon Shelah - 1997 - Annals of Pure and Applied Logic 85 (1):47-68.
Forcing with trees and order definability.Thomas J. Jech - 1975 - Annals of Mathematical Logic 7 (4):387.

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