Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Less than $2^{ω}$ many translates of a compact nullset may cover the real line

100%
Elekes M., Steprāns J.
Fundamenta Mathematicae
|
2004
|
tom 181
|
nr 1
89-96
EN
We answer a question of Darji and Keleti by proving that there exists a compact set C₀ ⊂ ℝ of measure zero such that for every perfect set P ⊂ ℝ there exists x ∈ ℝ such that (C₀+x) ∩ P is uncountable. Using this C₀ we answer a question of Gruenhage by showing that it is consistent with ZFC (as it follows e.g. from $cof(𝓝) < 2^{ω}$) that less than $2^{ω}$ many translates of a compact set of measure zero can cover ℝ.
2
Content available remote

The consistency of 𝔟 = κ and 𝔰 = κ⁺

100%
Fischer V., Steprāns J.
Fundamenta Mathematicae
|
2008
|
tom 201
|
nr 3
283-293
EN
Using finite support iteration of ccc partial orders we provide a model of 𝔟 = κ < 𝔰 = κ⁺ for κ an arbitrary regular, uncountable cardinal.
3
Content available remote

Possible cardinalities of maximal abelian subgroups of quotients of permutation groups of the integers

100%
Shelah S., Steprāns J.
Fundamenta Mathematicae
|
2007
|
tom 196
|
nr 3
197-235
EN
If G is a group then the abelian subgroup spectrum of G is defined to be the set of all κ such that there is a maximal abelian subgroup of G of size κ. The cardinal invariant A(G) is defined to be the least uncountable cardinal in the abelian subgroup spectrum of G. The value of A(G) is examined for various groups G which are quotients of certain permutation groups on the integers. An important special case, to which much of the paper is devoted, is the quotient of the full symmetric group by the normal subgroup of permutations with finite support. It is shown that, if we use G to denote this group, then A(G) ≤ 𝔞. Moreover, it is consistent that A(G) ≠ 𝔞. Related results are obtained for other quotients using Borel ideals.
4
Content available remote

Borel Tukey morphisms and combinatorial cardinal invariants of the continuum

81%
Coskey S., Mátrai T., Steprāns J.
Fundamenta Mathematicae
|
2013
|
tom 223
|
nr 1
29-48
EN
We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality 𝔭 ≤ 𝔟 does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting and splitting numbers. Lastly, we use our results to give an embedding from the inclusion ordering on 𝒫(ω) into the Borel Tukey ordering on cardinal invariants.
5
Content available remote

Universal functions

81%
Larson P., Miller A., Steprāns J., Weiss W.
Fundamenta Mathematicae
|
2014
|
tom 227
|
nr 3
197-245
EN
A function of two variables F(x,y) is universal if for every function G(x,y) there exist functions h(x) and k(y) such that G(x,y) = F(h(x),k(y)) for all x,y. Sierpiński showed that assuming the Continuum Hypothesis there exists a Borel function F(x,y) which is universal. Assuming Martin's Axiom there is a universal function of Baire class 2. A universal function cannot be of Baire class 1. Here we show that it is consistent that for each α with 2 ≤ α < ω₁ there is a universal function of class α but none of class β <α. We show that it is consistent with ZFC that there is no universal function (Borel or not) on the reals, and we show that it is consistent that there is a universal function but no Borel universal function. We also prove some results concerning higher-arity universal functions. For example, the existence of an F such that for every G there are h₁,h₂,h₃ such that for all x,y,z, G(x,y,z) = F(h₁(x),h₂(y),h₃(z)) is equivalent to the existence of a binary universal F, however the existence of an F such that for every G there are h₁,h₂,h₃ such that for all x,y,z, G(x,y,z) = F(h₁(x,y),h₂(x,z),h₃(y,z)) follows from a binary universal F but is strictly weaker.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.