Some theorems on vector spaces and the axiom of choice
Some topological consequences of the Product Measure Extension Axiom
Some topological properties of -covering sets
We prove the following theorems: There exists an -covering with the property . Under there exists such that is not an -covering or is not an -covering]. Also we characterize the property of being an -covering.
Some uniformization results
Some variations on the partition property for normal ultrafilters on Pkl
Suppose κ is a supercompact cardinal and λ≥κ. In [3], we studied the relationship between the weak partition property and the partition property for normal ultrafilters on . In this paper we study a hierarchy of properties intermediate between the weak partition property and the partition property. Given appropriate large cardinal assumptions, we show that these properties are not all equivalent.
Sorts Of Huge Cardinals
Spaces not distinguishing convergences.
Spaces not distinguishing convergences
In the present paper we introduce a convergence condition and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.
Spaces of urelements
Spaces of urelements, II
Spaces related to gamma-sets
Special issue: Editorial [Papers from 8th International Conference on Fuzzy Sets - Theory and Applications, FSTA 2006]
Special Issue: Editorial [Selected papers from 7th FSTA Conference, 2004]
Special Issue: Guest editorial [Summer School on Aggregation Operators, Related Techniques and Their Applications AGOP'2003]
Spectra of uniformity
We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform ultrafilters; we also show that this spectrum is not necessarily closed.
Splitting stationary sets in for λ with small cofinality
For a regular uncountable cardinal κ and a cardinal λ with cf(λ) < κ < λ, we investigate the consistency strength of the existence of a stationary set in which cannot be split into λ⁺ many pairwise disjoint stationary subsets. To do this, we introduce a new notion for ideals, which is a variation of normality of ideals. We also prove that there is a stationary set S in such that every stationary subset of S can be split into λ⁺ many pairwise disjoint stationary subsets.
Splitting -covers
The authors give a ZFC example for a space with but not .
Square bracket partition relations in L
Squares with diamonds and Souslin trees with special squares
Stable families of analytic sets
We give a different proof of the well-known fact that any uncountable family of analytic subsets of a Polish space with the point-finite intersection property must contain a subfamily whose union is not analytic. Our approach is based on the Kunen-Martin theorem.