Ultrafilter extensions of asymptotic density

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00504054" target="_blank" >RIV/67985840:_____/19:00504054 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.14712/1213-7243.2015.279" target="_blank" >http://dx.doi.org/10.14712/1213-7243.2015.279</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2015.279" target="_blank" >10.14712/1213-7243.2015.279</a>

Result language
angličtina
Original language name
Ultrafilter extensions of asymptotic density
Original language description
We characterize for which ultrafilters on $omega$ is the ultrafilter extension of the asymptotic density on natural numbers $sigma$-additive on the quotient boolean algebra $mathcal{P}(omega)/d_{mathcal{U}}$ or satisfies similar additive condition on $mathcal{P}(omega)/text{fin}$. These notions were defined in [Blass A., Frankiewicz R., Plebanek G., Ryll-Nardzewski C., {it A Note on extensions of asymptotic density}, Proc. Amer. Math. Soc. {bf 129} (2001), no. 11, 3313--3320] under the name ${boldsymbol{AP}}$(null) and ${boldsymbol{AP}}$(*). We also present a characterization of a $P$- and semiselective ultrafilters using the ultraproduct of $sigma$-additive measures.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF17-33849L" target="_blank" >GF17-33849L: Filters, Ultrafilters and Connections with Forcing</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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