Knaster and friends III: Subadditive colorings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575310" target="_blank" >RIV/67985840:_____/23:00575310 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/jsl.2022.50" target="_blank" >https://doi.org/10.1017/jsl.2022.50</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2022.50" target="_blank" >10.1017/jsl.2022.50</a>
Alternative languages
Result language
angličtina
Original language name
Knaster and friends III: Subadditive colorings
Original language description
We continue our study of strongly unbounded colorings, this time focusing on subadditive maps. In Part I of this series, we showed that, for many pairs of innite cardinals θ < κ, the existence of a strongly unbounded coloring c : [κ]2→ θ is a theorem of ZFC. Adding the requirement of subadditivity to a strongly unbounded coloring is a significant strengthening, though, and here we see that in many cases the existence of a subadditive strongly unbounded coloring c : [κ]2→ θ is independent of ZFC. We connect the existence of subadditive strongly unbounded colorings with a number of other infinitary combinatorial principles, including the narrow system property, the existence of κ-Aronszajn trees with ascent paths, and square principles. In particular, we show that the existence of a closed, subadditive, strongly unbounded coloring c : [κ]2→θ is equivalent to a certain weak indexed square principle ind(κ, 0). We conclude the paper with an application to the failure of the infinite productivity of κ-stationarily layered posets, answering a question of Cox.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Symbolic Logic
ISSN
0022-4812
e-ISSN
1943-5886
Volume of the periodical
88
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
51
Pages from-to
1230-1280
UT code for WoS article
000906855200001
EID of the result in the Scopus database
2-s2.0-85133659516