On the Rudin-Blass Ordering of Measures

2025/04/20 by Borodulin-Nadzieja, Piotr, Martínez-Celis, Arturo, Morawski, Adam +1
#03E05 (Primary) 03E35 #03E75 #28A33 #28E15 #46E27 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2504.14678

Abstract

We study the Rudin-Blass (and the Rudin-Keisler) ordering on the finite additive measures on ω. We propose a generalization of the notion of Q-point and selective ultrafilter to measures: Q-measures and selective measures. We show some symmetries between Q-points and Q-measures but also we show where those symmetries break up. In particular we present an example of a measure which is minimal in the sense of Rudin-Blass but which is not a Q-measure.

Citations

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Related

• On measures induced by forcing names for ultrafilters
• Density measures and additive property
• On embedding certain partial orders into the P-points under RK and Tukey reducibility
• The Rudin-Kisler ordering of P-points under \mathfrakb = \mathfrakc
• A few special ordinal ultrafilters