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Idempotent ultrafilters without Zorn’s lemma. (English) Zbl 1427.03053

Summary: We introduce the notion of additive filter and present a new proof of the existence of idempotent ultrafilters on \(\mathbb{N}\) without using Zorn’s Lemma in its entire power, and where one only assumes the ultrafilter theorem for the continuum.

MSC:

03E25 Axiom of choice and related propositions
03E05 Other combinatorial set theory
54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.)
05D10 Ramsey theory
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