As we know that in OSPF we need to have Area 0 and also aka Backbone Area. But In MPLS Domain the OSPF Backbone Area term had detached.
Instead of having Backbone Area, In MPLS Domain we have some thing known as Super Back Bone. The Service Provider network is Know as Super Backbone area in MPLS Domain, which replace you traditional OPSF backbone Area.
So as per Traditional OSPF design we supposed to have Area 0 but in MPLS domain Super Back bone area is not associated with any area number. So in MPLS domain OSPF can work without Area 0.
Below Document show that how OSPF is configured without Area 0
OSPF Without Area 0