HL ideals and Sacks indestructible ultrafilters

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00576354" target="_blank" >RIV/67985840:_____/24:00576354 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.apal.2023.103326" target="_blank" >https://doi.org/10.1016/j.apal.2023.103326</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2023.103326" target="_blank" >10.1016/j.apal.2023.103326</a>

Result language
angličtina
Original language name
HL ideals and Sacks indestructible ultrafilters
Original language description
We study ultrafilters on countable sets and reaping families which are indestructible by Sacks forcing. We deal with the combinatorial characterization of such families and we prove that every reaping family of size smaller than the continuum is Sacks indestructible. We prove that complements of many definable ideals are Sacks reaping indestructible, with one notable exception, the complement of the ideal Z of sets of asymptotic density zero. We investigate the existence of Sacks indestructible ultrafilters and prove that every Sacks indestructible ultrafilter is a Z-ultrafilter.
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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