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.

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  1. Definable element of a first-order structure
  2. Model of a first-order theory
  3. First-order structure
  4. First-order logic
  5. Mathematical logic
  6. Foundations of mathematics
  7. Area of mathematics
  8. Mathematics
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