P-measures in models without P-points
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929280842203136 |
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| author | Borodulin-Nadzieja, Piotr Cancino-Manríquez, Jonathan Morawski, Adam |
| author_facet | Borodulin-Nadzieja, Piotr Cancino-Manríquez, Jonathan Morawski, Adam |
| contents | We answer in negative the problem if the existence of a P-measure implies the existence of a P-point. Namely, we show that if we add random reals to a certain unique P-point model, then in the resulting model we will have a P-measure but not P-points. Also, we investigate the question if there is a P-measure in the Silver model. We show that rapid filters cannot be extended to a P-measure in the extension by $ω$ product of Silver forcings and that in the model obtained by the product of $ω_2$ many Silver forcings there are no P-measures of countable Maharam type |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14042 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | P-measures in models without P-points Borodulin-Nadzieja, Piotr Cancino-Manríquez, Jonathan Morawski, Adam Logic We answer in negative the problem if the existence of a P-measure implies the existence of a P-point. Namely, we show that if we add random reals to a certain unique P-point model, then in the resulting model we will have a P-measure but not P-points. Also, we investigate the question if there is a P-measure in the Silver model. We show that rapid filters cannot be extended to a P-measure in the extension by $ω$ product of Silver forcings and that in the model obtained by the product of $ω_2$ many Silver forcings there are no P-measures of countable Maharam type |
| title | P-measures in models without P-points |
| topic | Logic |
| url | https://arxiv.org/abs/2401.14042 |