Narrow systems revisited

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00586663" target="_blank" >RIV/67985840:_____/24:00586663 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1112/blms.13037" target="_blank" >https://doi.org/10.1112/blms.13037</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/blms.13037" target="_blank" >10.1112/blms.13037</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Narrow systems revisited

Popis výsledku v původním jazyce

We investigate connections between set-theoretic compactness principles and cardinal arithmetic, introducing and studying generalized narrow system properties as a way to approach two open questions about two-cardinal tree properties. The first of these questions asks whether the strong tree property at a regular cardinal (Formula presented.) implies the singular cardinals hypothesis ((Formula presented.)) above (Formula presented.). We show here that a certain narrow system property at (Formula presented.) that is closely related to the strong tree property, and holds in all known models thereof, suffices to imply (Formula presented.) above (Formula presented.). The second of these questions asks whether the strong tree property can consistently hold simultaneously at all regular cardinals (Formula presented.). We show here that the analogous question about the generalized narrow system property has a positive answer. We also highlight some connections between generalized narrow system properties and the existence of certain strongly unbounded subadditive colorings.

Název v anglickém jazyce

Narrow systems revisited

Popis výsledku anglicky

We investigate connections between set-theoretic compactness principles and cardinal arithmetic, introducing and studying generalized narrow system properties as a way to approach two open questions about two-cardinal tree properties. The first of these questions asks whether the strong tree property at a regular cardinal (Formula presented.) implies the singular cardinals hypothesis ((Formula presented.)) above (Formula presented.). We show here that a certain narrow system property at (Formula presented.) that is closely related to the strong tree property, and holds in all known models thereof, suffices to imply (Formula presented.) above (Formula presented.). The second of these questions asks whether the strong tree property can consistently hold simultaneously at all regular cardinals (Formula presented.). We show here that the analogous question about the generalized narrow system property has a positive answer. We also highlight some connections between generalized narrow system properties and the existence of certain strongly unbounded subadditive colorings.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04683S" target="_blank" >GA23-04683S: Kompaktnost v teorii množin a její aplikace v algebře a teorii grafů</a><br>

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

Bulletin of the London Mathematical Society

ISSN

0024-6093

e-ISSN

1469-2120

Svazek periodika

56

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

1967-1987

Kód UT WoS článku

001194040300001

EID výsledku v databázi Scopus

2-s2.0-85189641179