Theorems · Definition · logic and foundations
Ordinal.veblen
Ordinal.{u} → Ordinal.{u} → Ordinal.{u}veblen o is the o-th function in the Veblen hierarchy starting with ω ^ ·. That is:
- veblen 0 a = ω ^ a.
- veblen o for o ≠ 0 enumerates the fixed points of veblen o' for o' < o.
- Defined in
- Mathlib.SetTheory.Ordinal.Veblen
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 43 from the axioms · 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 and proof · cited by 1,688
- Ordinal.omega0proof · cited by 197
- Ordinal.veblenWithproof · cited by 34
Cited by67
Results whose statement or proof uses this declaration.
- Ordinal.gammaproof · cited by 27
- Ordinal.invVeblen₁proof · cited by 20
- Ordinal.epsilonproof · cited by 18
- Ordinal.veblen_zerostatement · cited by 10
- Ordinal.veblen_invVeblen₁_invVeblen₂statement · cited by 7
- Ordinal.veblen_zero_applystatement · cited by 6
- Ordinal.gamma_zero_eq_nfpstatement and proof · cited by 4
- Ordinal.veblen_eq_of_lt_invVeblen₁statement · cited by 4
- Ordinal.veblen_veblen_of_ltstatement · cited by 4
- Ordinal.veblen_zero_strictMonostatement · cited by 4
- Ordinal.invVeblen₁_veblenstatement and proof · cited by 4
- Ordinal.veblen_lt_veblen_iff_rightstatement · cited by 3