No coin nor oath required. For personal study only.
We prove, in ZFC alone, some new results on regularity and decomposability of ultrafilters. Generally, they have the form "Every (Ξ», ΞΌ)-regular ultrafilter is (Ξ» , ΞΌ )-regular and ΞΊ-decomposable", for various choices of the cardinals Ξ», ΞΌ, Ξ» , ΞΌ and ΞΊ. We also deal with products and sums of ultrafilters, we list some problems, and we furnish applications to topological spaces and to extended logics.
π SIMILAR VOLUMES
Applications of the ergodic iteration theorem I prove several natural preservation theorems for the countable support iteration. This solves a question of RosΕanowski regarding the preservation of localization properties and greatly simplifies the proofs in the area.
On some sets of dictionaries whose Ο-powers have a given complexity A dictionary is a set of finite words over some finite alphabet X. The Ο-power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V . Lecomte has recently studied the complexity of the set
## Groupwise density cannot be much bigger than the unbounded number We prove that g (the groupwise density number) is smaller or equal to b + , the successor of the minimal cardinality of an unbounded subset of Ο Ο. This is true even for the version of g for groupwise dense ideals.