In #14 Jonathan mentioned principal upsets for a given element of the poset. This can be easily generalized for sets instead of elements: for a poset \$$\(P, \leq$$\\) and \$$S \subseteq P\$$, we can define \$$\operatorname{\uparrow}(S) = \\{y \in P : s \in S \Longrightarrow y \ge s\\}\$$. I'm venturing:

**Puzzle JL1**: Can you give an example of [upper set](https://en.wikipedia.org/wiki/Upper_set) that *doesn't* arise this way?