  Everett's relative-state construction in quantum theory has never been
satisfactorily expressed in the Heisenberg picture. What one might have
expected to be a straightforward process was impeded by conceptual and
technical problems that we solve here. The result is a construction which,
unlike Everett's one in the Schr\"odinger picture, makes manifest the locality
of Everettian multiplicity, and its inherently approximative nature, and its
origin in certain kinds of entanglement and locally inaccessible information.
Our construction also allows us to give a more precise definition of an Everett
'universe', under which it is fully quantum, not quasi-classical, and we
compare the Everettian decomposition of a quantum state with the foliation of a
spacetime.
