  Objectivity constitutes one of the main features of the macroscopic classical
world. An important aspect of the quantum-to-classical transition issue is to
explain how such a property arises from the microscopic quantum world.
Recently, within the framework of open quantum systems, there has been proposed
such a mechanism in terms of the, so-called, Spectrum Broadcast Structures.
These are multipartite quantum states of the system of interest and a part of
its environment, assumed to be under an observation. This approach requires a
departure from the standard open quantum systems methods, as the environment
cannot be completely neglected. In the present work we study the emergence of
such a state-structures in one of the canonical models of the condensed matter
theory: Spin-boson model, describing the dynamics of a two-level system coupled
to an environment made up by a large number of harmonic oscillators. We pay
much attention to the behavior of the model in the non-Markovian regime, in
order to provide a testbed to analyze how the non-Markovian nature of the
evolution affects the surfacing of a spectrum broadcast structure.
