Does the class of linear orders have (one of the variants of) the so called (λ,κ)-limit model? It is necessarily unique, and naturally assuming some instances of G.C.H. we get some positive results. More generally, letting T be a complete first order theory and for simplicity assume G.C.H., for regular λ > κ > |T| does T have (variants of) a (λ,κ)-limit models, except for stable T? For some, yes, the theory of dense linear order, for some, no. Moreover, for independent T we get negative results. We deal more with linear orders.

Tbilisi Mathematical Journal, Vol. 7(1) (2014), pp. 99-128