The relation of rapid ultrafilters and Q-points to Van der Waerden ideal
The splitting number can be smaller than the matrix chaos number
Let χ be the minimum cardinality of a subset of that cannot be made convergent by multiplication with a single Toeplitz matrix. By an application of a creature forcing we show that < χ is consistent. We thus answer a question by Vojtáš. We give two kinds of models for the strict inequality. The first is the combination of an ℵ₂-iteration of some proper forcing with adding ℵ₁ random reals. The second kind of models is obtained by adding δ random reals to a model of for some δ ∈ [ℵ₁,κ). It...
There are absolute ultrafilters on N which are not minimal
Totally proper forcing and the Moore-Mrówka problem
We describe a totally proper notion of forcing that can be used to shoot uncountable free sequences through certain countably compact non-compact spaces. This is almost (but not quite!) enough to produce a model of ZFC + CH in which countably tight compact spaces are sequential-we still do not know if the notion of forcing described in the paper can be iterated without adding reals.
Two cases when and are equal
We deal with two cardinal invariants and give conditions on their equality using Shelah's pcf theory.
Two counterexamples concerning Hausdorff dimensions of projections
Type d'ordre des ordinaux de modèles non dénombrables de la théorie des ensembles
Undecidability of the existence of regular extremally disconnected S-spaces
Universal functions
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...
Very small sets
Weak variants of Martin's Axiom
Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of fixed points...
Whitehead Modules over Domains.
О возможном решении обобщенной континиум-проблемы.
О неразложимых -свободных абелевых группах.
Об интервалах и цепях в скелетах эпиморфности конгруэнц-дистрибутивных многообразий
Обобщенно-конструктивный континуум.