Indestructibility of some compactness principles over models of PFA

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00576355" target="_blank" >RIV/67985840:_____/24:00576355 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11210/24:10477924

Result on the web

<a href="https://doi.org/10.1016/j.apal.2023.103359" target="_blank" >https://doi.org/10.1016/j.apal.2023.103359</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apal.2023.103359" target="_blank" >10.1016/j.apal.2023.103359</a>

Result language

angličtina

Original language name

Indestructibility of some compactness principles over models of PFA

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GF19-29633L" target="_blank" >GF19-29633L: Compactness principles and combinatorics</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

1873-2461

Volume of the periodical

175

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

17

Pages from-to

103359

UT code for WoS article

001078824100001

EID of the result in the Scopus database

2-s2.0-85171791208