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Re: [ontolog-forum] HOL decidability [Was: using SKOS forcontrolled valu

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 14 Oct 2010 13:39:31 -0400
Message-id: <4CB74053.4010907@xxxxxxxxxxx>
On 10/14/2010 1:15 PM, Rich Cooper wrote:
> what I meant by the statement "there is no function that can iterate the
> primes", and perhaps I should have originally said "directly, without
> iterating other types", which seems to have set off this mess.    (01)

The word 'iterate' seems to be the trigger that created the mess.    (02)

I would interpret your wish in the following terms:    (03)

Find a closed-form expression that defines a function Pr(n), which
for any positive integer n produces the n-th prime.    (04)

In other words, you want a statement of the following form that
computes the n-th prime:    (05)

   Pr(n) = some algebraic expression that uses n, but does not
           contain any nested or implied loop or recursive function.    (06)

I agree that no such definition exists.    (07)

John    (08)

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