Are the following statements all equivalent?

  • Thread starter Bipolarity
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #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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