A Set-Theoretic Metaphysics for Wavefunction

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.