The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$

Dilip Raghavan

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arXiv · 1210.7387

The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$

Dilip Raghavan

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Abstract

We investigate the Tukey type of the generic ultrafilter added by the quotient $\mathcal{P}(ω\times ω) / (\mathrm{FIN} \times \mathrm{FIN})$. We prove that this ultrafilter is not basically generated and yet does not have the maximal Tukey type among directed partial orders of size continuum. Moreover, any Tukey reduction from this ultrafilter to any other ultrafilter is witnessed by a Baire class one map.

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BibTeX RIS

Dilip Raghavan. 2012-10-28. The generic ultrafilter added by ${(\FIN \times \FIN)}^{+}$. https://arxiv.org/abs/1210.7387

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