MHB Transfinite Induction: Theorem or Axiom?

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Is transfinite induction a theorem o an axiom?
 
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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).
 

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