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Is it consistent with ZF set theory without the Axiom of Choice that every ultrafilter on the natural numbers is a P-point?

Related: Rudin-Keisler ordering of ultrafilters, Shelah's theorem on the consistency of no P-points, Blass-Shelah theorem on ultrafilters and cardinal characteristics

In standard set theory with the Axiom of Choice, P-points are a special class of ultrafilters on the natural numbers that have strong regularity properties, allowing certain infinite partitions to be controlled in a coherent way. With the Axiom of Choice available, it is known that the existence of P-points is independent of ZFC, meaning some models have them and some do not. The question being raised here is what happens in the choiceless setting: when you remove the Axiom of Choice, the landscape of ultrafilters changes dramatically, and it becomes unclear whether all ultrafilters that can exist must be P-points, or whether non-P-point ultrafilters can still be constructed without choice-based machinery.

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