A sentence with closed-term parameters holds in a term model if and only if it belongs to the complete consistent theory defining that model. Prove this by structural induction: atoms are the definition, Boolean steps use completeness and consistency, and existential sentences use the Henkin witness property. Conversely any existential witness represented by a term gives the existential sentence by logical inference.

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  1. Term model
  2. Henkin construction
  3. Godel completeness theorem
  4. First-order logic
  5. Mathematical logic
  6. Foundations of mathematics
  7. Area of mathematics
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