Let * be a set-defined operation on N and consider *-closed cuts of N as horizons. We try to construct such a sequence that every horizon, preserving its limit, automatically preserves limits of all set-defined sequences, in the technique of alternative set theory. The main result is that such a construction is possible if and only if the starting horizon was a left-handed coast of some *-gap. The only possible universal horizon so is a right-handed coast of the same gap.