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arXiv · 2311.15492

On the Tukey types of Fubini products

Tom Benhamou·Natasha Dobrinen
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Abstract

We extend the class of ultrafilters $U$ over countable sets for which $U\cdot U\equiv_T U$, extending several results from \cite{Dobrinen/Todorcevic11}. In particular, we prove that for each countable ordinal $α\geq 2$, the generic ultrafilter $G_α$ forced by $P(ω^α)/\text{fin}^{\otimesα}$ satisfy $G_α\cdot G_α\equiv_T G_α$. This answers a question posed in \cite[Question 43]{Dobrinen/Todorcevic11}. Additionally, we establish that Milliken-Taylor ultrafilters possess the property that $U\cdot U\equiv_T U$.

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Tom Benhamou, Natasha Dobrinen. 2024-11-25. On the Tukey types of Fubini products. https://arxiv.org/abs/2311.15492

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