Gδ AND CO-MEAGER SEMIFILTERS
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Gδ AND CO-MEAGER SEMIFILTERS
Original language description
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.
Czech name
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Czech description
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Classification
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
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fundamenta Mathematicae
ISSN
0016-2736
e-ISSN
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Volume of the periodical
2016
Issue of the periodical within the volume
235
Country of publishing house
PL - POLAND
Number of pages
14
Pages from-to
153-166
UT code for WoS article
000387103300003
EID of the result in the Scopus database
2-s2.0-84984799274