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Ultrafilter extensions of asymptotic density

Jan Grebík (2019)

Commentationes Mathematicae Universitatis Carolinae

We characterize for which ultrafilters on ω is the ultrafilter extension of the asymptotic density on natural numbers σ -additive on the quotient boolean algebra 𝒫 ( ω ) / d 𝒰 or satisfies similar additive condition on 𝒫 ( ω ) / fin . These notions were defined in [Blass A., Frankiewicz R., Plebanek G., Ryll-Nardzewski C., A Note on extensions of asymptotic density, Proc. Amer. Math. Soc. 129 (2001), no. 11, 3313–3320] under the name A P (null) and A P (*). We also present a characterization of a P - and semiselective ultrafilters...

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