The following bare-bones story introduces the idea of a cumulative
hierarchy of pure sets: ‘Sets are arranged in stages. Every set is found at some stage.
At any stage S: for any sets found before S, we find a set whose members are exactly
those sets. We find nothing else at S.’ Surprisingly, this story already guarantees
that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity.
I show this by presenting Level Theory, a simplification of set theories due to Scott,
Montague, Derrick, and Potte
