Theorems · Definition · logic and foundations
Ordinal.veblenWith
(Ordinal.{u} → Ordinal.{u}) → Ordinal.{u} → Ordinal.{u} → Ordinal.{u}veblenWith f o is the o-th function in the Veblen hierarchy starting with f. This is
defined so that
- veblenWith f 0 = f.
- veblenWith f o for o ≠ 0 enumerates the common fixed points of veblenWith f o' over all
o' < o.
- Defined in
- Mathlib.SetTheory.Ordinal.Veblen
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 42 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
- Set.Iioproof · cited by 1,166
- Ordinal.derivFamilyproof · cited by 18
Cited by35
Results whose statement or proof uses this declaration.
- Ordinal.veblenproof · cited by 64
- Ordinal.veblenWith_right_strictMonostatement · cited by 9
- Ordinal.veblenWith_veblenWith_of_ltstatement and proof · cited by 9
- Ordinal.veblenWith_zerostatement · cited by 8
- Ordinal.veblenWith_zero_strictMonostatement and proof · cited by 6
- Ordinal.veblenWith_of_ne_zerostatement and proof · cited by 5
- Ordinal.isNormal_veblenWithstatement · cited by 4
- Ordinal.cmp_veblenWithstatement and proof · cited by 4
- Ordinal.right_le_veblenWithstatement · cited by 3
- Ordinal.veblenWith_add_onestatement and proof · cited by 3
- Ordinal.veblenWith_veblenWith_eq_veblenWith_iffstatement · cited by 3
- Ordinal.mem_range_veblenWithstatement and proof · cited by 2