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
Let X be set of ordinals expressible in some data type for ordinals such that < is computable and a∈X ∧ b<a → b∈X. Then sup(X) is computable
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Replying to @ModelOfTheory @ObjectOfObjects
Proof: the program computing < on that data type is a computation of sup(X).
5:17 PM - 24 Apr 2017
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