Narrow systems revisited
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Narrow systems revisited
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA23-04683S" target="_blank" >GA23-04683S: Compactness in set theory, with applications to algebra and graph theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bulletin of the London Mathematical Society
ISSN
0024-6093
e-ISSN
1469-2120
Volume of the periodical
56
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
1967-1987
UT code for WoS article
001194040300001
EID of the result in the Scopus database
2-s2.0-85189641179