I-ultrafilters in the rational perfect set model

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00585180" target="_blank" >RIV/67985840:_____/24:00585180 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1017/jsl.2022.81" target="_blank" >https://doi.org/10.1017/jsl.2022.81</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/jsl.2022.81" target="_blank" >10.1017/jsl.2022.81</a>

Result language
angličtina
Original language name
I-ultrafilters in the rational perfect set model
Original language description
We give a new characterization of the cardinal invariant d as the minimal cardinality of a family D of tall summable ideals such that an ultrafilter is rapid if and only if it has non-empty intersection with all the ideals in the family D . On the other hand, we prove that in the Miller model, given any family D of analytic tall p-ideals such that |D| < d , there is an ultrafilter U which is an I -ultrafilter for all ideals I is an element of D at the same time, yet U is not a rapid ultrafilter. As a corollary, we obtain that in the Miller model, given any analytic tall p-ideal I , I -ultrafilters are dense in the Rudin-Blass ordering, generalizing a theorem of Bartoszynski and S. Shelah, who proved that in such model, Hausdorff ultrafilters are dense in the Rudin-Blass ordering. This theorem also shows some limitations about possible generalizations of a theorem of C. Laflamme and J. Zhu.
Czech name
—
Czech description
—

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
—
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

Similar results(10)