Theorems · Theorem · logic and foundations
FirstOrder.Language.realize_iff_of_model_completeTheory
∀ {L : FirstOrder.Language} (M : Type w) (N : Type u_1) [inst : L.Structure M] [inst_1 : L.Structure N]
[N ⊨ L.completeTheory M] (φ : L.Sentence), N ⊨ φ ↔ M ⊨ φ- Defined in
- Mathlib.ModelTheory.Semantics
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Sentence.Realizestatement and proof · cited by 62
- FirstOrder.Language.completeTheorystatement and proof · cited by 14
- FirstOrder.Language.Theory.realize_sentence_of_memproof · cited by 11
- FirstOrder.Language.Sentence.realize_notproof · cited by 6
- FirstOrder.Language.mem_completeTheoryproof · cited by 3
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