  We study the emergence of decoherent histories in isolated systems based on
exact numerical integration of the Schr\"odinger equation for a Heisenberg
chain. We reveal that the nature of the system, which we switch from (i)
chaotic to (ii) interacting integrable to (iii) non-interacting integrable,
strongly impacts decoherence. From a finite size scaling law we infer a strong
exponential suppression of coherences for (i), a weak exponential suppression
for (ii) and no exponential suppression for (iii) on a relevant short
(nonequilibrium) time scale. Moreover, for longer times we find stronger
decoherence for (i) but the opposite for (ii), hinting even at a possible
power-law decay for (ii) at equilibrium time scales. This behaviour is encoded
in the multi-time properties of the quantum histories and it can not be
explained by environmentally induced decoherence. Our results suggest that
chaoticity plays a crucial role in the emergence of classicality in finite size
systems.
