Transfinite Induction: Theorem or Axiom?

[facenian1]

Is transfinite induction a theorem o an axiom?

 

[HOI]

That depends. In any logical system you can always take any given statement as an "axiom" (you might need to drop at least one other axiom to keep a "minimal" set of axioms) or as a theorem (you might need to add at least one other axiom to be able to prove the theorem).