The elements of V₄ - respectively the subsets of V₃ - ordered in a Hasse diagram by inclusion.

V₄ = P^4({}) = P( P( P(P({})))) is the powerset of the power set of the power set of the power set of the empty set.

As many brackets are usually hard to understand, the sets are defined by circles instead of brackets. The circle containing nothing stands for the empty set.

The universe (the thing all shown sets are a subset from) in this Hasse diagram is P^3({}) and expressed in set brackets it looks like this:

{ {} , {{}} , {{{}}} , {{},{{}}} }