0576355 - MÚ 2025 RIV NL eng J - Článek v odborném periodiku
Honzík, R. - Lambie-Hanson, Christopher - Stejskalová, Š.
Indestructibility of some compactness principles over models of PFA.
Annals of Pure and Applied Logic. Roč. 175, č. 1 (2024), č. článku 103359. ISSN 0168-0072. E-ISSN 1873-2461
Institucionální podpora: RVO:67985840
Klíčová slova: Guessing models * indestructibility * the tree property * weak Kurepa Hypothesis
Obor OECD: Pure mathematics
Impakt faktor: 0.6, rok: 2023
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.apal.2023.103359

We show that PFA (Proper Forcing Axiom) implies that adding any number of Cohen subsets of ω will not add an ω2-Aronszajn tree or a weak ω1-Kurepa tree, and moreover no σ-centered forcing can add a weak ω1-Kurepa tree (a tree of height and size ω1 with at least ω2 cofinal branches). This partially answers an open problem whether ccc forcings can add ω2-Aronszajn trees or ω1-Kurepa trees (with ¬□ω in the latter case). We actually prove more: We show that a consequence of PFA, namely the guessing model principle, GMP, which is equivalent to the ineffable slender tree property, ISP, is preserved by adding any number of Cohen subsets of ω. And moreover, GMP implies that no σ-centered forcing can add a weak ω1-Kurepa tree (see Section 2.1 for definitions). For more generality, we study variations of the principle GMP at higher cardinals and the indestructibility consequences they entail, and as applications we answer a question of Mohammadpour about guessing models at weakly but not strongly inaccessible cardinals and show that there is a model in which there are no weak ℵω+1-Kurepa trees and no ℵω+2-Aronszajn trees.
Trvalý link: https://hdl.handle.net/11104/0345924