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Indestructibility of some compactness principles over models of PFA
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SYSNO ASEP 0576355 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Indestructibility of some compactness principles over models of PFA Tvůrce(i) Honzík, R. (CZ)
Lambie-Hanson, Christopher (MU-W) SAI, ORCID
Stejskalová, Š. (CZ)Číslo článku 103359 Zdroj.dok. Annals of Pure and Applied Logic. - : Elsevier - ISSN 0168-0072
Roč. 175, č. 1 (2024)Poč.str. 17 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova Guessing models ; indestructibility ; the tree property ; weak Kurepa Hypothesis Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics Způsob publikování Omezený přístup Institucionální podpora MU-W - RVO:67985840 UT WOS 001078824100001 EID SCOPUS 85171791208 DOI https://doi.org/10.1016/j.apal.2023.103359 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2025 Elektronická adresa https://doi.org/10.1016/j.apal.2023.103359
Počet záznamů: 1