We find conditions on a function space \({\varvec{L}}\) that ensure that it behaves as an \(L_p\) -space in the sense that any unconditional basis of a complemented subspace of \({\varvec{L}}\) either is equivalent to the unit vector system of \(\ell _2\) or has a subbasis equivalent to a disjointly supported basic sequence. This dichotomy allows us to classify the symmetric basic sequences of \({\varvec{L}}\) . Several applications to Orlicz function spaces are provided.
