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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2212.14096 |
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| _version_ | 1866918238306172928 |
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| author | Benhamou, Tom |
| author_facet | Benhamou, Tom |
| contents | We improve Galvin's Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every $κ$-complete ultrafilter over a measurable cardinal $κ$ satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin $κ$-complete ultrafilters. Finally, we prove that $\diamondsuit(κ)$ implies the existence of a $κ$-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions \cite[Question 5.22]{TomMotiII},\cite[Question 3.4]{Non-GalvinFil} and questions ,\cite[Question 4.5]{BenGarShe},\cite[Question 2.26]{bgp}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14096 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Saturation Properties of Ultrafilters in Canonical Inner Models Benhamou, Tom Logic We improve Galvin's Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every $κ$-complete ultrafilter over a measurable cardinal $κ$ satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin $κ$-complete ultrafilters. Finally, we prove that $\diamondsuit(κ)$ implies the existence of a $κ$-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions \cite[Question 5.22]{TomMotiII},\cite[Question 3.4]{Non-GalvinFil} and questions ,\cite[Question 4.5]{BenGarShe},\cite[Question 2.26]{bgp}. |
| title | Saturation Properties of Ultrafilters in Canonical Inner Models |
| topic | Logic |
| url | https://arxiv.org/abs/2212.14096 |