Every strongly summable ultrafilter on $⨁{\mathbb{Z}}_2$ is sparse

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, Steprāns and Strauss.

This is the final version of a paper that contains the answer to a question that appeared in an article of Hindman, Steprāns 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

References in corpus (1)

• On strongly summable ultrafilters