The tree property and the continuum function below aleph_omega
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F16%3A10325730" target="_blank" >RIV/00216208:11210/16:10325730 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
The tree property and the continuum function below aleph_omega
Original language description
Starting from a Laver-indestructible supercompact $kappa$ and a weakly compact $lambda$ above $kappa$, we show there is a forcing extension where $kappa$ is a strong limit singular cardinal with cofinality $omega$, $2^kappa = kappa^{+3} = lambda^+$, and the tree property holds at $kappa^{++} = lambda$. Next we generalize this result to an arbitrary cardinal $mu$ such that $kappa <mathrm{cf}(mu)$ and $lambda^+ le mu$. This result provides more information about possible relationships between the tree property and the continuum function.
Czech name
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Czech description
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Classification
Type
O - Miscellaneous
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů