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
Answers can only be viewed under the following conditions:
 The questioner was satisfied with and accepted the answer, or
 The answer was evaluated as being 100% correct by the judge.
Alessandro Iraci
1.7K

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.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
 answered
 640 views
 $10.00
Related Questions
 InclusionExclusion and Generating Function with Coefficient (and Integer Equation)
 What is the asymptotic density of $A$ and $B$ which partition the reals into subsets of positive measure?
 Number of Combinations Created from Restricting a Set
 Proof through inclusion (A∆B) ∪ A = A ∪ B
 Discrete Math/ Set theory Question
 Souslin operation
 Recursive Set
 Set Theory Question Help