Theorems · Theorem · logic and foundations
Ordinal.lt_epsilon0
Deprecated since 2026-02-02Use Ordinal.lt_epsilon_zero instead.
∀ {o : Ordinal.{u}}, o < Ordinal.epsilon 0 ↔ ∃ n, o < (fun a => Ordinal.omega0 ^ a)^[n] 0Alias of Ordinal.lt_epsilon_zero.
ε₀ is the limit of 0, ω ^ 0, ω ^ ω ^ 0, …
- Defined in
- Mathlib.SetTheory.Ordinal.Veblen
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- Nat.iteratestatement · cited by 740
- Ordinal.omega0statement · cited by 197
- Ordinal.epsilonstatement · cited by 18
- Ordinal.lt_epsilon_zeroproof · cited by 1
Cited by0
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