On the Rudin-Blass Ordering of Measures
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917249875443712 |
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| author | Borodulin-Nadzieja, Piotr Martínez-Celis, Arturo Morawski, Adam Świerczyńska, Jadwiga |
| author_facet | Borodulin-Nadzieja, Piotr Martínez-Celis, Arturo Morawski, Adam Świerczyńska, Jadwiga |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Rudin-Blass Ordering of Measures Borodulin-Nadzieja, Piotr Martínez-Celis, Arturo Morawski, Adam Świerczyńska, Jadwiga Logic Classical Analysis and ODEs 03E05 (Primary) 03E35, 03E75, 28E15, 28A33, 46E27 (Secondary) 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. |
| title | On the Rudin-Blass Ordering of Measures |
| topic | Logic Classical Analysis and ODEs 03E05 (Primary) 03E35, 03E75, 28E15, 28A33, 46E27 (Secondary) |
| url | https://arxiv.org/abs/2504.14678 |