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by Maxatar
419 days ago
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Yeah for sure. If a sentence S is undecidable from your axioms for the natural numbers then there are two models A and B satisfying those axioms where A satisfies S and B satisfies not S. So which one is the standard natural numbers, is it A or B? Either A or B will be an example of something that satisfies your definition of natural numbers and yet is not the natural numbers. |
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