8 papers · 1 filter
On the complexity of Hamel bases of infinite dimensional Banach spaces
Lorenz Halbeisen
We call a subset S of a topological vector space V linearly Borel, if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It will…
Ultrafilter spaces on the semilattice of partitions
Lorenz Halbeisen, Benedikt Loewe
The Stone-Cech compactification of the natural numbers bN, or equivalently, the space of ultrafilters on the subsets of omega, is a well-studied space with interesting properties.…
Techniques for approaching the dual Ramsey property in the projective hierarchy
Lorenz Halbeisen, Benedikt Loewe
We define the dualizations of objects and concepts which are essential for investigating the Ramsey property in the first levels of the projective hierarchy, prove a forcing equiva…
Ramseyan ultrafilters
Lorenz Halbeisen
We investigate families of partitions of omega which are related to special coideals, so-called happy families, and give a dual form of Ramsey ultrafilters in terms of partitions.…
Symmetries between two Ramsey properties
Lorenz Halbeisen
In this article we compare the well-known Ramsey property with a dual form of it, the so called dual-Ramsey property (which was suggested first by Carlson and Simpson). Even if the…
On shattering, splitting and reaping partitions
Lorenz Halbeisen
In this article we investigate the dual-shattering cardinal H, the dual-splitting cardinal S and the dual-reaping cardinal R, which are dualizations of the well-known cardinals h (…