Primitive recursion, but using ordinals as bounds instead of integers (ie loops have an ordinal variable which must decrease each iteration)
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Replying to @ObjectOfObjects
Right. You would need a computable upper bound for the ordinals that can be used.
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Replying to @ModelOfTheory
Why does the upper bound need to be computable?
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Replying to @ObjectOfObjects @ModelOfTheory
If the upper bound is computable, you can guarantee the recursion terminates in finite time, I would think.
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Replying to @davidmanheim @ModelOfTheory
The assertion was that there *needs* to be a computable upper bound for *all* ordinals that can be used.
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Replying to @ObjectOfObjects @ModelOfTheory
right, because otherwise you can't guarantee that an arbitrary recursion terminates in finite time...
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Replying to @davidmanheim @ObjectOfObjects
No. There is no infinite descending sequence of ordinals at all. Restricting to computable ordinals is not necessary for that.
5:15 PM - 24 Apr 2017
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