  We compute the tail algebras of exchangeable monotone stochastic processes.
This allows us to prove the analogue of de Finetti's theorem for this type of
processes. In addition, since the vacuum state on the $q$-deformed
$C^*$-algebra is the only exchangeable state when $|q|<1$, we draw our
attention to its tail algebra, which turns out to obey a zero-one law.
