5 papers · 1 filter
Almost Kurepa Suslin trees and destructibility of the Guessing Model Property
Chris Lambie-Hanson, Šárka Stejskalová
Building on recent work of Krueger and the second author, we prove the consistency of the Guessing Model Principle at together with the existence of an almost Kurepa Suslin t…
A Strongly Non-Saturated Aronszajn Tree Without Weak Kurepa Trees
John Krueger, Šárka Stejskalová
Assuming the negation of Chang's conjecture, there is a c.c.c. forcing which adds a strongly non-saturated Aronszajn tree. Using a Mahlo cardinal, we construct a model in which the…
Kurepa trees, continuous images, and perfect set properties
Chris Lambie-Hanson, Šárka Stejskalová
Building upon work of Lücke and Schlicht, we study (higher) Kurepa trees through the lens of higher descriptive set theory, focusing in particular on various perfect set properties…
Club Stationary Reflection and other Combinatorial Principles at
Thomas Gilton, Šárka Stejskalová
In this paper we continue the study in [Gilton-Levine-Stejskalova] of compactness and incompactness principles at double successors, focusing here on the case of double successors…
Indestructibility of some compactness principles over models of PFA
Radek Honzik, Chris Lambie-Hanson, Šárka Stejskalová
We show that (Proper Forcing Axiom) implies that adding any number of Cohen subsets of will not add an -Aronszajn tree or a weak -Kurepa tree, and more…