Theorems · Theorem · logic and foundations
Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow
∀ {o : Ordinal.{u}},
Ordinal.IsPrincipal (fun x1 x2 => x1 * x2) o ↔ o ≤ 2 ∨ o ∈ Set.range fun x => Ordinal.omega0 ^ Ordinal.omega0 ^ xThe main characterization theorem for multiplicative principal ordinals.
- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- LT.lt.ne'proof · cited by 1,417
- le_or_gtproof · cited by 269
- Ordinal.omega0statement and proof · cited by 197
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Ordinal.one_lt_omega0proof · cited by 39
- Ordinal.opow_zeroproof · cited by 38
- not_lt_zeroproof · cited by 11
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3
- Ordinal.isPrincipal_add_of_isPrincipal_mulproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.principal_mul_iff_le_two_or_omega0_opow_opowproof · cited by 0