Strong tree properties, Kurepa trees, and guessing models

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11210/24:10477919

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Strong tree properties, Kurepa trees, and guessing models

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Strong tree properties, Kurepa trees, and guessing models

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Monatshefte für Mathematik

ISSN

0026-9255

e-ISSN

1436-5081

Svazek periodika

203

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

38

Strana od-do

111-148

Kód UT WoS článku

001106477500001

EID výsledku v databázi Scopus

2-s2.0-85178303166