Abstract:We construct in ZFC an ultrafilter $\fam \scrfam U \in \Bbb N^{\ast }$ such that for every one-to-one function $f : \Bbb N\rightarrow \Bbb N$ there exists $U\in \fam \scrfam U$ with $f[U]$ in the summable ideal, i.e. the sum of reciprocals of its elements converges. This strengthens Gryzlov's result concerning the existence of $0$-points.
Keywords: ultrafilter, $0$-point, summable ideal, linked family
AMS Subject Classification: 54D40, 54G99