On the Tukey types of Fubini products
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917848106926080 |
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| author | Benhamou, Tom Dobrinen, Natasha |
| author_facet | Benhamou, Tom Dobrinen, Natasha |
| contents | 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 $U\cdot U\equiv_T U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_15492 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Tukey types of Fubini products Benhamou, Tom Dobrinen, Natasha Logic 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 $U\cdot U\equiv_T U$. |
| title | On the Tukey types of Fubini products |
| topic | Logic |
| url | https://arxiv.org/abs/2311.15492 |