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Ultrafilters on ????-their ideals and their cardinal characteristics
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For a free ultrafilter
U
\mathcal {U}
on
ω
\omega
we study several cardinal characteristics which describe part of the combinatorial structure of
U
\,\mathcal {U}
. We provide various consistency results; e.g. we show how to force simultaneously many characters and many
π
\pi
–characters. We also investigate two ideals on the Baire space
ω
ω
\omega ^{\omega }
naturally related to
U
\mathcal {U}
and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.
American Mathematical Society (AMS)
Title: Ultrafilters on ????-their ideals and their cardinal characteristics
Description:
For a free ultrafilter
U
\mathcal {U}
on
ω
\omega
we study several cardinal characteristics which describe part of the combinatorial structure of
U
\,\mathcal {U}
.
We provide various consistency results; e.
g.
we show how to force simultaneously many characters and many
π
\pi
–characters.
We also investigate two ideals on the Baire space
ω
ω
\omega ^{\omega }
naturally related to
U
\mathcal {U}
and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.
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