Hi Matthew, nice application of the categoricity theorem! One question if I may. You said:

> In fact, while they are not isomorphic as lattices, they are in fact isomorphic as mere posets as you intuited.

But in my understanding the lattice and poset structure is inter-translatable as in [here](https://en.wikipedia.org/wiki/Lattice_(order)#Connection_between_the_two_definitions). Can two lattices be isomorphic and their associated posets not?