Idempotent ultrafilters without Zorn’s Lemma

Di Nasso, Mauro; Tachtsis, Eleftherios

doi:10.1090/proc/13719

Idempotent ultrafilters without Zorn’s Lemma
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by Mauro Di Nasso and Eleftherios Tachtsis PDF

Proc. Amer. Math. Soc. 146 (2018), 397-411 Request permission

Abstract:

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.

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