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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.14096 |
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Table of 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}.