## Jana Fla\v {s}kov\'a

*More than a 0-point *

Comment.Math.Univ.Carolin. 47,4 (2006) 617-621. **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

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