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arXiv · 2511.01050

Tukey-idempotency and strong p-points

Tom Benhamou·Natasha Dobrinen·Tan Özalp
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Abstract

We characterize strong $p$-point ultrafilters by showing that they are exactly those $p$-points that are not Tukey above $(\omega^\omega,\leq)$; 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 Hru\v{s}\'ak 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}.

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Tom Benhamou, Natasha Dobrinen, Tan Özalp. 2025-11-02. Tukey-idempotency and strong p-points. https://arxiv.org/abs/2511.01050

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