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Countable ordinals
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Large countable ordinals
First infinite ordinal
ω
Epsilon numbers
ε
0
Feferman–Schütte ordinal
Γ
0
Ackermann ordinal
θ
(Ω
2
)
small Veblen ordinal
θ
(Ω
ω
)
large Veblen ordinal
θ
(Ω
Ω
)
Bachmann–Howard ordinal
ψ
(
ε
Ω+1
)
Buchholz's ordinal
ψ
0
(Ω
ω
)
Takeuti–Feferman–Buchholz ordinal
ψ
(
ε
Ω
ω
+1
)
Proof-theoretic ordinals of
the theories of iterated inductive definitions
Computable ordinals
< ω
CK
1
Nonrecursive ordinal
≥ ω
CK
1
First uncountable ordinal
Ω
