INDESTRUCTIBILITY OF THE TREE PROPERTY

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F20%3A10422936" target="_blank" >RIV/00216208:11210/20:10422936 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=N-Wt2GNq-D" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=N-Wt2GNq-D</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2019.61" target="_blank" >10.1017/jsl.2019.61</a>

Result language
angličtina
Original language name
INDESTRUCTIBILITY OF THE TREE PROPERTY
Original language description
In the first part of the article, we show that if omega = <= kappa < lambda are cardinals, kappa(<kappa) = kappa, and lambda is weakly compact, then in V[M(kappa, lambda)] the tree property at lambda = (kappa(++))(V[M(kappa,lambda)]) is indestructible under all kappa(+)-cc forcing notions which live in V[Add(kappa, lambda)], where Add(kappa, lambda) is the Cohen forcing for adding lambda-many subsets of kappa and M(kappa, lambda) is the standard Mitchell forcing for obtaining the tree property at lambda = (kappa(++))(V[M(kappa, lambda)]). This result has direct applications to Prikry-type forcing notions and generalized cardinal invariants. In the second part, we assume that lambda is supercompact and generalize the construction and obtain a model V*, a generic extension of V, in which the tree property at (kappa(++))(V)* is indestructible under all kappa(+)-cc forcing notions living in V[Add(kappa, lambda)], and in addition under all forcing notions living in V* which are kappa(+)-closed and "liftable" in a prescribed sense (such as kappa(++)-directed closed forcings or well-met forcings which are kappa(++)-closed with the greatest lower bounds).
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF19-29633L" target="_blank" >GF19-29633L: Compactness principles and combinatorics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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