[HTML][HTML] Pathology of submeasures and ideals
J Mart�nez, D Meza-Alc�ntara, C Uzc�tegui�- Archive for Mathematical�…, 2024 - Springer
J Mart�nez, D Meza-Alc�ntara, C Uzc�tegui
Archive for Mathematical Logic, 2024•SpringerWe address some phenomena about the interaction between lower semicontinuous
submeasures on N and F σ ideals. We analyze the pathology degree of a submeasure and
present a method to construct pathological F σ ideals. We give a partial answers to the
question of whether every nonpathological tall F σ ideal is Katětov above the random ideal
or at least has a Borel selector. Finally, we show a representation of nonpathological F σ
ideals using sequences in Banach spaces.
submeasures on N and F σ ideals. We analyze the pathology degree of a submeasure and
present a method to construct pathological F σ ideals. We give a partial answers to the
question of whether every nonpathological tall F σ ideal is Katětov above the random ideal
or at least has a Borel selector. Finally, we show a representation of nonpathological F σ
ideals using sequences in Banach spaces.
Abstract
We address some phenomena about the interaction between lower semicontinuous submeasures on and ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological ideals. We give a partial answers to the question of whether every nonpathological tall ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological ideals using sequences in Banach spaces.
Springer