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Idempotent ultrafilters without Zorn's Lemma

Authors: Mauro Di Nasso and Eleftherios Tachtsis
Journal: Proc. Amer. Math. Soc. 146 (2018), 397-411
MSC (2010): Primary 03E25, 03E05, 54D80; Secondary 05D10
Published electronically: August 1, 2017
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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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Additional Information

Mauro Di Nasso
Affiliation: Dipartimento di Matematica, Università di Pisa, Pisa 56126, Italy

Eleftherios Tachtsis
Affiliation: Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece

Keywords: Algebra on $\beta\mathbb{N}$, idempotent ultrafilters, ultrafilter theorem
Received by editor(s): November 25, 2016
Received by editor(s) in revised form: February 19, 2017
Published electronically: August 1, 2017
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2017 American Mathematical Society

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