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Topic: Order-preserving embeddings of ordinals in the real numbers
Replies: 18   Last Post: Aug 12, 2006 10:03 AM

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john baez

Posts: 460
Registered: 12/6/04
Re: Order-preserving embeddings of ordinals in the real numbers
Posted: Aug 6, 2006 9:09 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <1154768360.892279.285400@m79g2000cwm.googlegroups.com>,
Keith Ramsay <kramsay@aol.com> wrote:

>John Baez wrote:

>|I believe that for every countably infinite ordinal X below
>|the Church-Turing ordinal, there's a enumeration of X such
>|that the order relation on X becomes a recursive relation on X.
>|Is this right?


>I assume the Church-Turing ordinal is the same as the one
>often known as the Church-Kleene ordinal.


Sorry! I seem to have a Pavlovian tendency to write "Turing"
when I see "Church-". I've made that mistake several times.
I see now it led me into learning about Turing's thesis work
with Church on "Systems of logic defined by ordinals".
When I heard about this, I assumed it dealt with the
"Church-Turing ordinal". I should have been saying
"Church-Kleene ordinal" all along. I'll fix "week236".

>Yes. It can be made primitive recursive even.

Thanks!





Date Subject Author
7/28/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
victor_meldrew_666@yahoo.co.uk
8/2/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
john baez
8/3/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
tchow@lsa.umich.edu
8/4/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
bogus address
8/5/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Aatu Koskensilta
8/6/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Aatu Koskensilta
8/7/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Bill Taylor
8/7/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Aatu Koskensilta
8/11/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Keith Ramsay
8/12/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Aatu Koskensilta
8/8/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Daryl McCullough
8/8/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Patricia Shanahan
8/8/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Daryl McCullough
8/8/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
tchow@lsa.umich.edu
8/5/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
tchow@lsa.umich.edu
8/7/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Keith Ramsay
8/5/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Keith Ramsay
8/6/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
john baez

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