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:: This merely cites the same paper you cite above by Tait. There's really no additional content there. And, as a side note, I don't know if I'd count the FOMlist as a reliable source ;) [[User:AshtonBenson|AshtonBenson]] ([[User talk:AshtonBenson|talk]]) 04:09, 28 August 2009 (UTC)
:I guess I don't understand Astonbenson's notion of "notable", or "important".
:: Please see [http://en.wikipedia.org/wiki/Wikipedia:Notability WP:NOTABILITY] :The following is certainly ''historically'' important. So I'll offer it up: :Hilbert viewed "recursion" ("primitive", the only kind known at the time he gave his 1928) as the keystone of his formal, axiomatic theory of arithmetic. Hilbert (1926) had conjectured that there might be functions that could not be generated by [''primitive''] recursion, but Ackermann had not yet presented his (1928) novel "double-recursion", nor had Péter (1935) [reference: Kleene 1952:271]. So, Hilbert, in his 1927 ''The foundations of mathematics'' (van Heijenoort pp. 464ff) had only ''primitive'' recursion (based on Peano's successor and induction) at his disposal. He says "Finally, we also need ''explicit definitions'', . . . as well as certain ''recursion axioms'', which result from a general recursion schema. . . . For in my theory contentual inference is replaced by manipulation of signs according to rules; '''in this way the axiomatic method attains that reliability and perfection that it can and must reach if it is to become the basic instrument of all theoretical research'''."(boldface added, p. 467) He goes on about a page later to define what he means by "recursion" (nothing surprising -- the previous calculation is employed in generating the next calculation see p. 468), and after that, he states "In a corresponding way, the recursion axioms are formula systems that are modeled upon the recursive procedure. ¶ These are the general foundations of my theory. To familiarize you with the way in which it is applied I would like to adduce some examples of particular functions as they are defined by recursion." (p. 469) Here he offers examples of simple recursions starting with ι(0)=0; ι(a')=1, [etc].
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