Joel David Hamkins (@joeldavidhamkins): "Here is the recursive definition of the natural sum of ordinals. I give five different accounts of the natural sum, proceeding from different philosophies about how we best engage with the ordinals. But they are all equivalent, which is a happy situation for mathematical insight."

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Here is the recursive definition of the natural sum of ordinals. I give five different accounts of the natural sum, proceeding from different philosophies about how we best engage with the ordinals. But they are all equivalent, which is a happy situation for mathematical insight.

Let us next provide a recursive definition of the natural sum. Namely, we define the recursive natural sum α ⊕ β to be the first ordinal that is larger than α’ ⊕ β and α ⊕ β’ for all smaller ordinals α’ < α and β’ < β.

Joel David Hamkins

Mar 18

2:36 PM

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