Theorems · Definition · logic and foundations
Ordinal.omega0
Ordinal.{u}ω is the first infinite ordinal, defined as the order type of ℕ.
Conventions for notations in identifiers:
* The recommended spelling of ω in identifiers is omega0.
- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 197 results in Mathlib
- Foundations
- Depth 30 from the axioms, rests on 304 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- Ordinal.typeproof · cited by 207
- Ordinal.liftproof · cited by 86
Cited by201
Results whose statement or proof uses this declaration.
- Cardinal.alephproof · cited by 76
- Ordinal.veblenproof · cited by 64
- Ordinal.omegaproof · cited by 60
- Ordinal.one_lt_omega0statement and proof · cited by 39
- Cardinal.bethproof · cited by 35
- Ordinal.natCast_lt_omega0statement · cited by 24
- Ordinal.lt_omega0statement · cited by 15
- Ordinal.omega0_posstatement · cited by 14
- Ordinal.lift_omegaproof · cited by 12
- Ordinal.omega0_ne_zerostatement · cited by 10
- Ordinal.veblen_zerostatement and proof · cited by 10
- Ordinal.isSuccLimit_omega0statement and proof · cited by 9
Showing the 200 most cited of 201.