Michael Kosterlitz and David Thouless tried to resolve a contradiction about 2D crystals: on one hand side, the Mermin-Wagner theorem claims that symmetry breaking of a continuous order-parameter cannot exist in two dimensions. This implies, that perfect long range positional order is ruled out in 2D crystals. On the other side, very early computer simulations of Berni Alder and Thomas E. Wainwright indicated crystallization in 2D. The KTHNY theory shows implicitly that periodicity is not a necessary criterion for a solid (this is already indicated by the existence of amorphous solids like glasses). Following M. Kosterlitz, a finite shear elasticity defines a 2D solid, including quasicrystals in this description.