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%2F18%3A10325736" target="_blank" >RIV/00216208:11210/18:10325736 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/malq.201600028" target="_blank" >https://doi.org/10.1002/malq.201600028</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/malq.201600028" target="_blank" >10.1002/malq.201600028</a>
Alternative languages
Result language
angličtina
Original language name
The tree property and the continuum function below aleph_omega
Original language description
We say that a regular cardinal $kappa$, $kappa> aleph_0$, has the tree property if there are no $kappa$-Aronszajn trees; we say that $kappa$ has the weak tree property if there are no special $kappa$-Aronszajn trees. Starting with infinitely many weakly compact cardinals, we show that the tree property at every even cardinal $aleph_{2n}$, $0aleph_{2n+1}$, $n<omega$. Next, starting with infinitely many Mahlo cardinals, we show that the weak tree property at every cardinal $aleph_n$, $1 < n <omega$, is consistent with an arbitrary continuum function which satisfies $2^{aleph_n} > aleph_{n+1}$, $n<omega$. Thus the tree property has no provable effect on the continuum function below $aleph_omega$ except for the trivial requirement that the tree property at $kappa^{++}$ implies $2^kappa>kappa^+$ for every infinite $kappa$.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF15-34700L" target="_blank" >GF15-34700L: The continuum, forcing and large cardinals</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Logic Quarterly
ISSN
0942-5616
e-ISSN
—
Volume of the periodical
2018
Issue of the periodical within the volume
64
Country of publishing house
DE - GERMANY
Number of pages
14
Pages from-to
89-102
UT code for WoS article
000431504500007
EID of the result in the Scopus database
2-s2.0-85045416027