On wide Aronszajn trees in the presence of MA

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00544057" target="_blank" >RIV/67985840:_____/21:00544057 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/jsl.2020.42" target="_blank" >https://doi.org/10.1017/jsl.2020.42</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2020.42" target="_blank" >10.1017/jsl.2020.42</a>

Result language
angličtina
Original language name
On wide Aronszajn trees in the presence of MA
Original language description
A wide Aronszajn tree is a tree of size and height with no uncountable branches. We prove that under there is no wide Aronszajn tree which is universal under weak embeddings. This solves an open question of Mekler and Väänänen from 1994. We also prove that under, every wide Aronszajn tree weakly embeds in an Aronszajn tree, which combined with a result of Todorčević from 2007, gives that under every wide Aronszajn tree embeds into a Lipschitz tree or a coherent tree. We also prove that under there is no wide Aronszajn tree which weakly embeds all Aronszajn trees, improving the result in the first paragraph as well as a result of Todorčević from 2007 who proved that under there are no universal Aronszajn trees.
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/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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