Rigid first-order structure
= Rigid first-order structure
A first-order structure is rigid when its identity map is its only automorphism. Every finite linear order is rigid, whereas $(\mathbb Z,<)$ is nonrigid because every translation is an order automorphism.
Rigidity here means absence of nonidentity <automorphisms of a first-order structure>; it does not assert the mechanical rigidity of a rod-and-hinge framework.