Normal function
In
axiomatic set theory, a function
f :
Ord → Ord is called
normal (or a
normal function)
iff it is
continuous and
strictly mononotically increasing. That is, a function is normal iff the following two conditions hold:
- For every limit ordinal γ, f(γ) = {f(ν) : ν < γ}.
- For all ordinals α < β, f(α) < f(β).
It is easy to show that normal functions have arbitrarily large fixed points; see
Fixed-point lemma for normal functions for a proof.