κ-Lindelöf κ-stratifiable spaces are κ-metrizable

SMALL u κ AND LARGE 2 κ FOR SUPERCOMPACT κ

Garti and Shelah [2] state that one can force uκ to be κ+ for supercompact κ with 2κ arbitrarily large, using the technique of Džamonja and Shelah [1]. Here we spell out how this can be done. §

Compactification of κ-Frames

Hahn - Banach theorems for κ - normed spaces

For a new class of topological vector spaces, namely κ-normed spaces, an associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a κ-norm, that is a distance function between a point and a G δ-subset. For it, analogs of the Hahn-Banach theorem are proved.

Cardinal characteristics at κ in a small u(κ) model

We provide a model where u(κ) < 2κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that...

Every (λ, Κ)-regular Ultrafilter Is (λ, Κ)-regular

We prove the following: Theorem A. If D is a (λ+, κ)-regular ultrafilter, then either (a) D is (λ, κ)-regular, or (b) the cofinality of the linear order ∏ D〈λ, <〉 is cf κ, and D is (λ, κ′)-regular for all κ′ < κ. Corollary B. Suppose that κ is singular, κ > λ and either λ is regular, or cf κ < cf λ. Then every (λ+n, κ)-regular ultrafilter is (λ, κ)-regular. We also discuss some consequences and...