\(I\)-ultrafilters were introduced by J. Baumgartner in 1995. In this talk, under the continuum hypothesis, we show the following results:
- (1) There is a discrete ultrafilter which is not a \(Z_0\)-ultrafilter.
- (2) There is a \(\sigma\)-compact ultrafilter which is not a \(Z_0\)-ultrafilter.
- (3) There is a \(J_3^\omega\) ultrafilter which is not a \(Z_0\)-ultrafilter, where \(Z_0\) is the ideal of subsets of \(\omega\) with asymptotic density zero.
This is joint work with Jianyong Hong.