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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.
π SIMILAR VOLUMES
## More on regular and decomposable ultrafilters in ZFC 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»
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