  We demonstrate that hidden long range order is always present in the gapped
phases of interacting fermionic systems on one dimensional lattices. It is
captured by correlation functions of appropriate nonlocal charge and/or spin
operators, which remain asymptotically finite. The corresponding microscopic
orders are classified. The results are confirmed by DMRG numerical simulation
of the phase diagram of the extended Hubbard model, and of a Haldane insulator
phase.
