Abstract
Under CH we show the following results:(1)There is a discrete ultrafilter which is not a $${\mathcal {Z}}_{0}$$Z0-ultrafilter.(2)There is a $$\sigma $$ź-compact ultrafilter which is not a $${\mathcal {Z}}_{0}$$Z0-ultrafilter.(3)There is a $${\mathcal {J}}_{\omega ^{3}}$$Jź3-ultrafilter which is not a $${\mathcal {Z}}_{0}$$Z0-ultrafilter.
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