Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/proc/13719
Published electronically: August 1, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03E25, 03E05, 54D80, 05D10

Retrieve articles in all journals with MSC (2010): 03E25, 03E05, 54D80, 05D10


Additional Information

Mauro Di Nasso
Affiliation: Dipartimento di Matematica, Università di Pisa, Pisa 56126, Italy
Email: mauro.di.nasso@unipi.it

Eleftherios Tachtsis
Affiliation: Department of Mathematics, University of the Aegean, Karlovassi 83200, Samos, Greece
Email: ltah@aegean.gr

DOI: https://doi.org/10.1090/proc/13719
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

American Mathematical Society