Re: Computable functions/reals.

Frederick Williams <frederick.williams2@xxxxxxxxx> writes:

Bill Taylor wrote:

BUT, AFAIK, there is NO standard, accepted, agreed way
of extending it to computable functions of type f:R->R .

Have you seen

C Spector "Provably recursive functions of analysis..." in
_Recursive Function Theory_ ed J C E Dekker, being
Symposia in Pure Mathematics, V, AMS, 1962

?

What do you find in Spector's article that is relevant to Bill's
query?

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Aatu Koskensilta (aatu.koskensilta@xxxxxx)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

Relevant Pages

  • Re: Computable functions/reals.
    ... can extend Turing machines the way Mr. Ullrich or anyone else does. ... machines are intuively computable functions on N and all intuively ... all recursive functions on N are turing machines. ... That would make a mockery of everything Godel was up to." ...
    (sci.logic)
  • Re: Computable functions/reals.
    ... abstraction or extension, IMHO, by the Church-Turing thesis. ... can extend Turing machines the way Mr. Ullrich or anyone else does. ... machines are intuively computable functions on N and all intuively ... all recursive functions on N are turing machines. ...
    (sci.logic)
  • Re: Computable functions/reals.
    ... C Spector "Provably recursive functions of analysis..." ... Nothing, I haven't read it, but the title looked vaguely relevant. ...
    (sci.logic)