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Are the following statements all equivalent?

  1. Oct 11, 2013 #1
    1) Peano axioms for the natural numbers
    2) Well-ordering principle
    3) Principle of mathematical induction
    4) Principle of complete induction

    Are they all equivalent? I'm going to attempt to prove them if they are, but I'd like someone to point out whether they are or not. I've heard that they are but I may be wrong. Thanks!

    BiP
     
  2. jcsd
  3. Oct 11, 2013 #2

    Simon Bridge

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    All statements are equivalent for a given definition of "equivalent". :D
    You may find that some of them are consequences of another with some extra restrictions.
     
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