Gδ AND CO-MEAGER SEMIFILTERS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F16%3A10314906" target="_blank" >RIV/00216208:11210/16:10314906 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.impan.pl/shop/publication/transaction/download/product/91586" target="_blank" >https://www.impan.pl/shop/publication/transaction/download/product/91586</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/fm182-2-2016" target="_blank" >10.4064/fm182-2-2016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Gδ AND CO-MEAGER SEMIFILTERS

Popis výsledku v původním jazyce

The ultrafilters on the partial order ([ω]ω , SUBSET OF OR EQUAL TO ASTERISK OPERATOR ) are the free ultrafilters on ω, which constitute the space ω ASTERISK OPERATOR , the Stone-Cech remainder of ω. If U is an upperset of this partial order (i.e., a semifilter ), then the ultrafilters on U correspond to closed subsets of ω ASTERISK OPERATOR via Stone duality. If U is large enough, then it is possible to get combinatorially nice ultrafilters on U by generalizing the corresponding constructions for [ω]ω . In particular, if U is co-meager then there are ultrafilters on U that are weak P-filters (extending a result of Kunen). If U is Gδ (and hence also co-meager) and d = c then there are ultrafilters on U that are P-filters (extending a result of Ketonen). For certain choices of U , these constructions have applications in dynamics, algebra, and combinatorics. Most notably, we give a new proof of the fact that there are minimal-maximal idempotents in (ω*, +). This was an outstanding open problem solved only last year by Zelenyuk.

Název v anglickém jazyce

Gδ AND CO-MEAGER SEMIFILTERS

Popis výsledku anglicky

The ultrafilters on the partial order ([ω]ω , SUBSET OF OR EQUAL TO ASTERISK OPERATOR ) are the free ultrafilters on ω, which constitute the space ω ASTERISK OPERATOR , the Stone-Cech remainder of ω. If U is an upperset of this partial order (i.e., a semifilter ), then the ultrafilters on U correspond to closed subsets of ω ASTERISK OPERATOR via Stone duality. If U is large enough, then it is possible to get combinatorially nice ultrafilters on U by generalizing the corresponding constructions for [ω]ω . In particular, if U is co-meager then there are ultrafilters on U that are weak P-filters (extending a result of Kunen). If U is Gδ (and hence also co-meager) and d = c then there are ultrafilters on U that are P-filters (extending a result of Ketonen). For certain choices of U , these constructions have applications in dynamics, algebra, and combinatorics. Most notably, we give a new proof of the fact that there are minimal-maximal idempotents in (ω*, +). This was an outstanding open problem solved only last year by Zelenyuk.

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

2016

Kód důvěrnosti údajů

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

Název periodika

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

—

Svazek periodika

2016

Číslo periodika v rámci svazku

235

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

14

Strana od-do

153-166

Kód UT WoS článku

000387103300003

EID výsledku v databázi Scopus

2-s2.0-84984799274