 Pointwise definable model

Every element of a pointwise definable model is uniquely specified by a formula with no added parameters. Finite tuples are then uniquely specified by conjunctions of their defining formulas. For a complete theory these formulas isolate the tuple types, so such a model is an atomic model. The converse fails: a countable dense linear order without endpoints with a named point is atomic, while its other points are moved by structure automorphisms fixing that point.