On the Tukey types of Fubini products

2023/11/27 by Tom Benhamou, Benhamou, Tom, Natasha Dobrinen +1 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Graph Labeling and Dimension Problems #Logic (math.LO) #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2311.15492

openalex publication_date 2023/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the class of ultrafilters U over countable sets for which U⋅ U≡_T U, extending several results from \citeDobrinen/Todorcevic11. In particular, we prove that for each countable ordinal α≥ 2, the generic ultrafilter G_α forced by P(ω^α)/fin^⊗α satisfy G_α⋅ G_α≡_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⋅ U≡_T U.

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