Theorems · Theorem · logic and foundations
FirstOrder.Language.ElementaryEmbedding.theory_model_iff
∀ {L : FirstOrder.Language} {M : Type u_1} {N : Type u_2} [inst : L.Structure M] [inst_1 : L.Structure N]
(f : L.ElementaryEmbedding M N) (T : L.Theory), M ⊨ T ↔ N ⊨ T- Defined in
- Mathlib.ModelTheory.ElementaryMaps
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Theorystatement and proof · cited by 154
- FirstOrder.Language.Sentenceproof · cited by 127
- FirstOrder.Language.Theory.Modelstatement · cited by 67
- FirstOrder.Language.Sentence.Realizeproof · cited by 62
- FirstOrder.Language.ElementaryEmbeddingstatement and proof · cited by 33
- FirstOrder.Language.ElementaryEmbedding.map_sentenceproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_geproof · cited by 1