MHB Transfinite Induction: Theorem or Axiom?

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Transfinite induction can be classified as either a theorem or an axiom, depending on the logical system in use. In any system, a statement can be treated as an axiom, though this may require dropping another axiom to maintain minimality. Conversely, it can also be considered a theorem, which might necessitate the addition of another axiom for proof. The classification ultimately hinges on the foundational framework being applied. Thus, the status of transfinite induction is context-dependent.
facenian1
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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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