Prove a set is wellordered
Let $FS(α, β) ⇋ { f  f : β>α & Fin( {γ  γ ∈ β & not( f(γ) = 0 ) })}$ for all ordinals α, β,
where Fin(A) means the set A is finite.
We define a relation ≺ on FS: $f ≺ g ←→ (∃γ < β)( f(γ) < g(γ) & (∀δ < β)( γ < δ ⇒ f(δ) = g(δ)))$.
How to prove that (FS, ⪯) is wellordered?
Answer
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Alessandro Iraci
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On the second step of the induction you mean FS(L, B) = FS(L, Г) x L are isomorphic right?

Yes, exactly.
The answer is accepted.
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