Ultrafilter extensions of asymptotic density

0504054 - MÚ 2020 RIV CZ eng J - Journal Article
Grebík, Jan
Ultrafilter extensions of asymptotic density.
Commentationes Mathematicae Universitatis Carolinae. Roč. 60, č. 1 (2019), s. 25-37. ISSN 0010-2628
R&D Projects: GA ČR GF17-33849L
Institutional support: RVO:67985840
Keywords : asymptotic density * P-ultrafilter
OECD category: Pure mathematics
Method of publishing: Limited access
http://dx.doi.org/10.14712/1213-7243.2015.279

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.
Permanent Link: http://hdl.handle.net/11104/0295765