  Set theory brought revolution to philosophy of mathematics and it can bring
revolution to philosophy of physics too. All that stands in the way is the
intuition that sets of physical objects cannot themselves be physical objects,
which appears to derive from the ubiquitous assumption that it is possible for
there to exist numerically distinct observers in qualitatively identical
cognitive states. Overturning that assumption allows construing the
wavefunction of an elementary particle as being a set of elemental particles
with definite properties. A free electron in an observers universe is a set of
elemental electrons on different trajectories, each in an elemental parallel
universe. For any region in an observers environment which includes part of the
environmental electrons wavefunction there is a subset of elemental electrons
located in parallel elemental regions. The measure of that subset on the set
which is the environmental electron is the absolute square of quantum amplitude
for the environmental region. Decoherence induces Everettian branching as the
partitioning of wavefunction into subsets whose measures are the objective
probabilities of quasi-classical events within branches. Phase arises through
interactions between elemental universes, as with Many Interacting Worlds
theory, the difference being that an observers environment is constituted by a
set of worlds. That environment contains superpositions as sets of elemental
particle configurations.
