  This document comprises Level Theory, parts 1-3.
  PART 1. 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
simplifiation of set theories due to Scott, Montague, Derrick, and Potter.
  PART 2. Potentialists think that the concept of set is importantly modal.
Using tensed language as an heuristic, the following bare-bones story
introduces the idea of a potential hierarchy of sets: 'Always: for any sets
that existed, there is a set whose members are exactly those sets; there are no
other sets.' Surprisingly, this story already guarantees well-foundedness and
persistence. Moreover, if we assume that time is linear, the ensuing modal set
theory is almost definitionally equivalent with non-modal set theories;
specifically, with Level Theory, as developed in Part 1.
  PART 3. On a very natural conception of sets, every set has an absolute
complement. The ordinary cumulative hierarchy dismisses this idea outright. But
we can rectify this, whilst retaining classical logic. Indeed, we can develop a
boolean algebra of sets arranged in well-ordered levels. I show this by
presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part
1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly
implement Conway's games and surreal numbers; and an obvious extension of BLT
is definitionally equivalent with ZF.
