I-ultrafilters in the rational perfect set model

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

I-ultrafilters in the rational perfect set model

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

I-ultrafilters in the rational perfect set model

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Symbolic Logic

ISSN

0022-4812

e-ISSN

1943-5886

Svazek periodika

89

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

20

Strana od-do

175-194

Kód UT WoS článku

000952600000001

EID výsledku v databázi Scopus

2-s2.0-85144508026