Degrees of rigidity for Souslin trees
Joel David Hamkins (The City University of New York), Gunter Fuchs, (Westf\"alische Wilhelms-Universit\"at M\"unster)
TL;DR
This paper explores different levels of rigidity in Souslin trees, establishing a hierarchy, and applies these concepts to show how automorphism towers of certain groups can be manipulated via forcing under Diamond.
Contribution
It introduces a hierarchy of rigidity notions for Souslin trees and connects these to the automorphism tower problem in group theory using forcing techniques.
Findings
Established a hierarchy of rigidity notions for Souslin trees.
Demonstrated that automorphism towers can be made highly malleable by forcing.
Applied the hierarchy to the automorphism tower problem under Diamond.
Abstract
We investigate various strong notions of rigidity for Souslin trees, separating them under Diamond into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under Diamond that there is a group whose automorphism tower is highly malleable by forcing.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Advanced Operator Algebra Research