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Aug 8, 2023 at 21:54 comment added Andreas Blass The existence of Ramsey ultrafilters is independent of ZFC. Do you know what happens if there are no Ramsey ultrafilters? (If the OP had forgotten to say "non-principal" in the question, this would be trivial: The bottom element of the RK order (the class of principal ultrafilters) would not be the lower part of a gap.
Nov 3, 2017 at 7:18 vote accept Dominic van der Zypen
Nov 2, 2017 at 23:10 history answered Jing Zhang CC BY-SA 3.0