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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...

Ultrafilter with $ℵ_{0}$ predecessors in Rudin-Frolík order

Lev Bukovský, Eva Butkovičová (1981)

Commentationes Mathematicae Universitatis Carolinae

Ultrafilters and endomorphic universes

Athanossios Tzouvaras (1986)

Commentationes Mathematicae Universitatis Carolinae

Ultrafilters without immediate predecessors in Rudin-Frolík order

Eva Butkovičová (1982)

Commentationes Mathematicae Universitatis Carolinae

Ultrafiltres absolus et problèmes d'extraction de sous-suites

Alain Louveau (1973/1974)

Séminaire Choquet. Initiation à l'analyse

Undecidability of the existence of regular extremally disconnected S-spaces

Andrzej Szymański (1980)

Colloquium Mathematicae

Uniformization and anti-uniformization properties of ladder systems

Todd Eisworth, Gary Gruenhage, Oleg Pavlov, Paul Szeptycki (2004)

Fundamenta Mathematicae

Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The...

Uniformly completely Ramsey sets

Udayan Darji (1993)

Colloquium Mathematicae

Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also hold for uniformly...

Uniqueness of means in the Cohen model

Damjan Kalajdzievski, Juris Steprāns (2019)

Commentationes Mathematicae Universitatis Carolinae

We investigate the question of whether or not an amenable subgroup of the permutation group on $ℕ$ can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.

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