Order asymptotically isometric copies of l∞, l1 and c0 in Banach function spaces

We investigate order asymptotically isometric copies of c0, l∞ and l1 in Köthe spaces. Firstly we prove a number of general relations between them and we discuss what happens with such copies while passing to Köthe dual spaces, or vice versa - passing to preduals. Finally, we apply the results to characterize certain classes of Köthe spaces as Orlicz spaces, Calderón-LozanovskiÄ­ spaces, Orlicz-Lorentz spaces and Musielak-Orlicz spaces with such copies.