Theorems · Theorem · logic and foundations
FirstOrder.Language.dlo_age
∀ (M : Type w') [inst : FirstOrder.Language.order.Structure M] [Mdlo : M ⊨ FirstOrder.Language.order.dlo] [Nonempty M],
FirstOrder.Language.order.age M = {M | Finite ↑M ∧ ↑M ⊨ FirstOrder.Language.order.linearOrderTheory}- Defined in
- Mathlib.ModelTheory.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderproof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- Finitestatement and proof · cited by 3,029
- Set.extproof · cited by 2,266
- FirstOrder.Language.Structurestatement and proof · cited by 775
- CategoryTheory.Bundled.αstatement and proof · cited by 736
- Nonempty.someproof · cited by 340
- FirstOrder.Language.Embeddingproof · cited by 128
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- CategoryTheory.Bundledstatement and proof · cited by 42
- FirstOrder.Language.Structure.FGproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.isFraisseLimit_of_countable_nonempty_dloproof · cited by 2