  We study separable system-environment evolutions of pure dephasing type in
the context of objectivity and find that it can lead to the natural emergence
of Spectrum Broadcast Structure (SBS) states at discrete instances of time.
Contrary to the standard way of obtaining SBS states which requires
entanglement with the observed environment, reaching such states here does not
require decoherence (no unobserved environements are necessary). Yet the
biggest difference is the basis with respect to which the SBS states are
formed. Here it is not the pointer basis of the system given by the interaction
with the environment, but an equal superposition basis of said pointer states.
The price to pay is the momentary character of the formed SBS structures, hence
the term "glimpse".
