Theorems · Definition · logic and foundations
Cardinal.ord
Cardinal.{u} → Ordinal.{u}The ordinal corresponding to a cardinal c is the least ordinal whose cardinal is c.
- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 266 results in Mathlib
- Foundations
- Depth 41 from the axioms, rests on 498 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- iInfproof · cited by 1,690
- Ordinalstatement · cited by 1,688
- Ordinal.typeproof · cited by 207
- IsWellOrderproof · cited by 171
Cited by320
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgumentstatement · cited by 49
- Ordinal.IsInitialproof · cited by 28
- Cardinal.card_ordstatement and proof · cited by 23
- Cardinal.IsRegular.cof_ordstatement · cited by 23
- CategoryTheory.SmallObject.objstatement and proof · cited by 22
- Ordinal.bddAbove_of_smallproof · cited by 19
- Field.Emb.Cardinal.leastExtstatement and proof · cited by 13
- Field.Emb.Cardinal.wellOrderedBasisstatement · cited by 13
- Cardinal.lt_ordstatement · cited by 13
- Cardinal.mul_eq_selfproof · cited by 13
- Ordinal.IsFundamentalSequenceproof · cited by 12
- Cardinal.isSuccLimit_ordstatement and proof · cited by 11
Showing the 200 most cited of 320.