Number of the records: 1
Indestructibility of some compactness principles over models of PFA
- 1.
SYSNO ASEP 0576355 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Indestructibility of some compactness principles over models of PFA Author(s) Honzík, R. (CZ)
Lambie-Hanson, Christopher (MU-W) SAI, ORCID
Stejskalová, Š. (CZ)Article number 103359 Source Title Annals of Pure and Applied Logic. - : Elsevier - ISSN 0168-0072
Roč. 175, č. 1 (2024)Number of pages 17 s. Language eng - English Country NL - Netherlands Keywords Guessing models ; indestructibility ; the tree property ; weak Kurepa Hypothesis Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 001078824100001 EID SCOPUS 85171791208 DOI https://doi.org/10.1016/j.apal.2023.103359 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2025 Electronic address https://doi.org/10.1016/j.apal.2023.103359
Number of the records: 1