Theorems · Theorem · logic and foundations
Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow
Deprecated since 2026-03-17Use Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow instead.
∀ {o : Ordinal.{u}},
Ordinal.IsPrincipal (fun x1 x2 => x1 * x2) o ↔ o ≤ 2 ∨ o ∈ Set.range fun x => Ordinal.omega0 ^ Ordinal.omega0 ^ xAlias of Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow.
The main characterization theorem for multiplicative principal ordinals.
- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
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 · cited by 4,705
- Ordinalstatement · cited by 1,688
- Ordinal.omega0statement · cited by 197
- Ordinal.IsPrincipalstatement · cited by 92
- Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opowproof · cited by 1
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