Strong tree properties, Kurepa trees, and guessing models

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00581546" target="_blank" >RIV/67985840:_____/24:00581546 - isvavai.cz</a>

Alternative codes found

RIV/00216208:11210/24:10477919

Result on the web

<a href="https://doi.org/10.1007/s00605-023-01922-2" target="_blank" >https://doi.org/10.1007/s00605-023-01922-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00605-023-01922-2" target="_blank" >10.1007/s00605-023-01922-2</a>

Result language

angličtina

Original language name

Strong tree properties, Kurepa trees, and guessing models

Original language description

We investigate the generalized tree properties and guessing model properties introduced by Weiß and Viale, as well as natural weakenings thereof, studying the relationships among these properties and between these properties and other prominent combinatorial principles. We introduce a weakening of Viale and Weiß’s Guessing Model Property, which we call the Almost Guessing Property, and prove that it provides an alternate formulation of the slender tree property in the same way that the Guessing Model Property provides and alternate formulation of the ineffable slender tree property. We show that instances of the Almost Guessing Property have sufficient strength to imply, for example, failures of square or the nonexistence of weak Kurepa trees. We show that these instances of the Almost Guessing Property hold in the Mitchell model starting from a strongly compact cardinal and prove a number of other consistency results showing that certain implications between the principles under consideration are in general not reversible. In the process, we provide a new answer to a question of Viale by constructing a model in which, for all regular θ≥ ω2 , there are stationarily many ω2 -guessing models M∈Pω2H(θ) that are not ω1 -guessing models.

Czech name

—

Czech description

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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

Result was created during the realization of more than one project. More information in the Projects tab.

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

Monatshefte für Mathematik

ISSN

0026-9255

e-ISSN

1436-5081

Volume of the periodical

203

Issue of the periodical within the volume

1

Country of publishing house

AT - AUSTRIA

Number of pages

38

Pages from-to

111-148

UT code for WoS article

001106477500001

EID of the result in the Scopus database

2-s2.0-85178303166