Every strongly summable ultrafilter on $\bigoplus\mathbb Z_2$ is sparse
Logic
2013-03-26 v2 General Topology
Abstract
We investigate the possibility of the existence of nonsparse strongly summable ultrafilters on certain abelian groups. In particular, we show that every strongly summable ultrafilter on the countably infinite Boolean group is sparse. This answers a question of Hindman, Stepr\=ans and Strauss.
Keywords
Cite
@article{arxiv.1302.5676,
title = {Every strongly summable ultrafilter on $\bigoplus\mathbb Z_2$ is sparse},
author = {David J. Fernández Bretón},
journal= {arXiv preprint arXiv:1302.5676},
year = {2013}
}
Comments
This is the final version of a paper that contains the answer to a question that appeared in an article of Hindman, Stepr\=ans and Strauss (Semigroups in which all Strongly Summable Ultrafilters are Sparse, New York J. Math. 18 (2012), 835-848. Zbl pre06098874). It is also available via http://nyjm.albany.edu/j/2013/19-8.html