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In TI the quantum state is ontic, but quantum states describe offer waves of specific micro-degrees of freedom excited states of the underlying field. Since collapse occurs when an offer wave is absorbed–at the micro-level–there is no universal quantum state. A quantum state is not the correct description of the spacetime universe, since it is not a quantum object. This explains the emergence of the macro-level (in my interp., spacetime itself) as objects (clusters of actualized spacetime events) supervenient on actualized transactions (collapses). For a review of this point about spacetime emergence, and relevant references, see http://transactionalinterpretation.org/2015/03/10/a-unified-account-of-relativistic-and-non-relativistic-quantum-theory/
This is also discussed in my CUP book: http://www.cambridge.org/us/knowledge/discountpromotion/?site_locale=en_US&code=L2TIQM
And in conceptual terms in my new ICP book: http://www.worldscientific.com/worldscibooks/10.1142/p993
I should add that I certainly agree that decoherence occurs (as a deductive consequence of QM) in objects to which quantum states legitimately apply (such as bound states of fields, e.g. atoms). But I disagree that it is needed for a solution to the measurement problem in PTI, in which collapse generates spacetime events (classical phenomena).
Thanks again for your interest.