All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 17

Displaying 321 – 338 of 338

Showing per page

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...

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.

Vector sets with no repeated differences

Péter Komjáth (1993)

Colloquium Mathematicae

We consider the question when a set in a vector space over the rationals, with no differences occurring more than twice, is the union of countably many sets, none containing a difference twice. The answer is “yes” if the set is of size at most ℵ 2 , “not” if the set is allowed to be of size ( 2 2 ℵ 0 ) + . It is consistent that the continuum is large, but the statement still holds for every set smaller than continuum.

Weak Rudin-Keisler reductions on projective ideals

Konstantinos A. Beros (2016)

Fundamenta Mathematicae

We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of Hjorth’s theorem on the existence of a complete Π¹₁ equivalence relation. This proof enables us (under PD) to generalize Hjorth’s result to the classes of Π ¹ 2 n + 1 equivalence relations.

Weak square sequences and special Aronszajn trees

John Krueger (2013)

Fundamenta Mathematicae

A classical theorem of set theory is the equivalence of the weak square principle □ μ * with the existence of a special Aronszajn tree on μ⁺. We introduce the notion of a weak square sequence on any regular uncountable cardinal, and prove that the equivalence between weak square sequences and special Aronszajn trees holds in general.

Weakly normal ideals ou PKl and the singular cardinal hypothesis

Yoshihiro Abe (1993)

Fundamenta Mathematicae

In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay’s theorem concerning strongly compact cardinals, we show that λ < κ is decided if P κ λ carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.

When does the Katětov order imply that one ideal extends the other?

Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca (2013)

Colloquium Mathematicae

We consider the Katětov order between ideals of subsets of natural numbers (" ≤ K ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which ≤ K ⇒ ⊑ for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).

σ-Entangled linear orders and narrowness of products of Boolean algebras

Saharon Shelah (1997)

Fundamenta Mathematicae

We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts.

Currently displaying 321 – 338 of 338

Previous Page 17