Geodesic
Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property
Canadian journal of mathematics, Tome 68 (2016) no. 1, pp. 44-66

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DOI

We answer two questions of Hindman, Steprāns, and Strauss; namely, we prove that every strongly summable ultrafilter on an abelian group is sparse and has the trivial sums property. Moreover, we show that in most cases the sparseness of the given ultrafilter is a consequence of its being isomorphic to a union ultrafilter. However, this does not happen in all cases; we also construct (assuming Martin's Axiom for countable partial orders, i.e., $\operatorname{cov}\left( \text{M} \right)=\mathfrak{c})$ , a strongly summable ultrafilter on the Boolean group that is not additively isomorphic to any union ultrafilter.
DOI : 10.4153/CJM-2015-023-9
Mots-clés : 03E75, 54D35, 54D80, 05D10, 05A18, 20K99, ultrafilter, Stone–Čech compactification, sparse ultrafilter, strongly summable ultrafilter, union ultrafilter, finite sum, additive isomorphism, trivial sums property, Boolean group, abelian group 
Bretón, David J. Fernández. Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property. Canadian journal of mathematics, Tome 68 (2016) no. 1, pp. 44-66. doi: 10.4153/CJM-2015-023-9
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