  A crucial question is how objective and classical behavior arises from a
fundamental physical theory. Here we provide a natural definition of a
decoherence process valid in all causal theories, and show how its behavior can
be extremely different from the quantum one. Remarkably, despite this, we prove
that the so-called spectrum broadcast structure characterizes all objective
states in every fundamental causal theory, exactly as in quantum mechanics. Our
results show a stark contrast between the extraordinarily diverse decoherence
behavior and the universal features of objectivity.
