Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.IsComplete.isComplete_iff_models_elementarily_equivalent
∀ {L : FirstOrder.Language} {T : L.Theory},
T.IsComplete ↔ T.IsSatisfiable ∧ ∀ (M N : T.ModelType), L.ElementarilyEquivalent ↑M ↑NA theory is complete iff it is satisfiable and all its models are elementarily equivalent.
- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- FirstOrder.Language.Theory.ModelType.Carrierstatement and proof · cited by 59
- FirstOrder.Language.Theory.ModelsBoundedFormulaproof · cited by 30
- FirstOrder.Language.Theory.IsSatisfiablestatement and proof · cited by 25
- FirstOrder.Language.ElementarilyEquivalentstatement and proof · cited by 19
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