On the Isbell problem

Jonathan Cancino-Manríquez; Jindrich Zapletal

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arXiv · 2410.08699

On the Isbell problem

Jonathan Cancino-Manríquez·Jindrich Zapletal

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Abstract

We present three models concerning Tukey types of ultrafilters on $\omega$. The first model is built via a countable support iteration, and we show there is no basically generated ultrafilter in such model. The second and third models are built upon different and novel techniques, and in such models all ultrafilters are Tukey top, thus providing an answer to the Isbell problem. In all models there is no $\mathsf{nwd}$-ultrafilter.

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BibTeX RIS

Jonathan Cancino-Manríquez, Jindrich Zapletal. 2024-10-11. On the Isbell problem. https://arxiv.org/abs/2410.08699

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