Tukey-idempotency and strong p-points
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917055217795072 |
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| author | Benhamou, Tom Dobrinen, Natasha Özalp, Tan |
| author_facet | Benhamou, Tom Dobrinen, Natasha Özalp, Tan |
| contents | We characterize strong $p$-point ultrafilters by showing that they are exactly those $p$-points that are not Tukey above $(ω^ω,\leq)$; or equivalently, those $p$-points that are not Tukey-idempotent. Moreover, we show that there are no Canjar ultrafilters on measurable cardinals. We make use of tools which were motivated by topological Ramsey spaces, developed in \cite{Benhamou/Dobrinen24}, and furthermore, show that ultrafilters arising from most of the known topological Ramsey spaces are Tukey-idempotent. Our results answer questions of Hrušák and Verner \cite[Question 5.7]{Hrusak/Verner11}, Brook-Taylor \cite[Question 3.6]{QuestionGeneralized}, and partially Benhamou and Dobrinen \cite[Question 5.6]{Benhamou/Dobrinen24}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tukey-idempotency and strong p-points Benhamou, Tom Dobrinen, Natasha Özalp, Tan Logic 03E05, 03E04, 03E02, 05D10, 05C55, 06A06, 06A07 We characterize strong $p$-point ultrafilters by showing that they are exactly those $p$-points that are not Tukey above $(ω^ω,\leq)$; or equivalently, those $p$-points that are not Tukey-idempotent. Moreover, we show that there are no Canjar ultrafilters on measurable cardinals. We make use of tools which were motivated by topological Ramsey spaces, developed in \cite{Benhamou/Dobrinen24}, and furthermore, show that ultrafilters arising from most of the known topological Ramsey spaces are Tukey-idempotent. Our results answer questions of Hrušák and Verner \cite[Question 5.7]{Hrusak/Verner11}, Brook-Taylor \cite[Question 3.6]{QuestionGeneralized}, and partially Benhamou and Dobrinen \cite[Question 5.6]{Benhamou/Dobrinen24}. |
| title | Tukey-idempotency and strong p-points |
| topic | Logic 03E05, 03E04, 03E02, 05D10, 05C55, 06A06, 06A07 |
| url | https://arxiv.org/abs/2511.01050 |