It is widely thought that decoherence solves the measurement problem in a Many Worlds approach to quantum theory. In fact, this is claimed to be settled science in many internet sites with information on quantum theory. But this is not correct. Those ‘Quantum Darwinism’ arguments depend on smuggling in a hidden premise that is inconsistent with the basic Many Worlds approach. The culprit is phase randomness, which is a requirement to derive the decoherence allegedly supporting Quantum Darwinism, but which is not available in the Many Worlds picture. So there isn’t really a solution to the problem of ‘Schrodinger’s Cat’ in that interpretation. (There is however a solution if you really do have phase randomness and collapse, as in the transactional interpretation.) This new publication spells out the problem for decoherence-based accounts: http://philsci-archive.pitt.edu/10757/
Transactional Interpretation 