
Re: Orderpreserving embeddings of ordinals in the real numbers
Posted:
Aug 6, 2006 9:09 PM


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 ChurchTuring 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 ChurchTuring ordinal is the same as the one >often known as the ChurchKleene 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 "ChurchTuring ordinal". I should have been saying "ChurchKleene ordinal" all along. I'll fix "week236".
>Yes. It can be made primitive recursive even.
Thanks!

