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Is there a proof (in ZFC for instance) of the soundness of Peano Arithmetic?By "soundness" I mean that all theorems of Peano Arithmetic are true.

Thanks, Patrick

Patrick Clot
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    It's pretty straightforward to establish the soundness of peano arithmetic under the mapping $M(0) = {}$, $M(S(n)) = M(n) \cup {M(n)}$, then just one by one establish that the axioms of PA are theorems of ZFC. – DanielV Dec 13 '16 at 00:21
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    Yes. The proof in ZFC is a straightforward induction over the standard model of the natural numbers. See Landau's Foundations of Analysis or Halmos's Naive Set Theory for nice presentations. – Rob Arthan Dec 13 '16 at 00:25
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    I'm surprised this question was closed as off-topic - it's definitely a question about mathematics, and I'm not sure what additional context is needed (this is a naturally-occurring, interesting question; IMO it doesn't require explicit motivvation). I've voted to reopen. – Noah Schweber Dec 30 '16 at 20:30

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