Ultrafilters on 𝜔-their ideals and their cardinal characteristics

Shelah, Saharon; Brendle, Jörg; Shelah, Saharon

doi:10.1090/S0002-9947-99-02257-6

Ultrafilters on $\omega$-their ideals and their cardinal characteristics
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by Saharon Shelah, Jörg Brendle and Saharon Shelah

Trans. Amer. Math. Soc. 351 (1999), 2643-2674

DOI: https://doi.org/10.1090/S0002-9947-99-02257-6

Published electronically: March 8, 1999

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Abstract:

For a free ultrafilter $\mathcal {U}$ on $\omega$ we study several cardinal characteristics which describe part of the combinatorial structure of $\mathcal {U}$. We provide various consistency results; e.g. we show how to force simultaneously many characters and many $\pi$–characters. We also investigate two ideals on the Baire space $\omega ^{\omega }$ naturally related to $\mathcal {U}$ and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.

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