Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.exists_large_model_of_infinite_model
∀ {L : FirstOrder.Language} (T : L.Theory) (κ : Cardinal.{w}) (M : Type w') [inst : L.Structure M] [M ⊨ T] [Infinite M],
∃ N, Cardinal.lift.{max u v w, w} κ ≤ Cardinal.mk ↑NAny theory with an infinite model has arbitrarily large models.
- Defined in
- Mathlib.ModelTheory.Satisfiability
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.univproof · cited by 3,945
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- le_reflproof · cited by 2,061
- FirstOrder.Languagestatement and proof · cited by 1,084
- Cardinal.mkstatement and proof · cited by 942
- FirstOrder.Language.Structurestatement and proof · cited by 775
- Cardinal.liftstatement and proof · cited by 583
- le_of_eqproof · cited by 366
- Infinitestatement and proof · cited by 352
- FirstOrder.Language.Theorystatement and proof · cited by 154
- Set.subset_union_leftproof · cited by 142
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.exists_elementaryEmbedding_card_eq_of_geproof · cited by 1