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Topic: This Week's Finds in Mathematical Physics (Week 236)
Replies: 29   Last Post: Aug 24, 2006 9:00 AM

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john baez

Posts: 460
Registered: 12/6/04
Re: This Week's Finds in Mathematical Physics (Week 236)
Posted: Aug 8, 2006 4:09 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <1154931929.924105.82850@n13g2000cwa.googlegroups.com>,
Keith Ramsay <kramsay@aol.com> wrote:

>I don't think it's so hard to see that the way one ordinarily proves
>induction up to Gamma_0 is impredicative. It's not that it's impossible
>to define it predicatively. Each computable ordinal can be defined
>as an ordering on natural numbers, given by a primitive recursive
>relation on them. The existence of this ordering isn't the problem.
>The problem is proving induction up to it. The way that one ordinarily
>does it makes reference to sets of ordinals. That's the gist of it. To
>show that this is not a merely apparent obstacle to a predicative
>proof is a longer story.


I'd love to hear a bit more of the story, especially if you can tell
it in a charming and not too rigorous manner. In particular, nothing
in the paragraph says what's special about Gamma_0. For example,
suppose I have an ordinal smaller than Gamma_0. How can I give a
"predicative" proof of induction up to that ordinal? What breaks
down at Gamma_0?







Date Subject Author
7/26/06
Read This Week's Finds in Mathematical Physics (Week 236)
baez@math.removethis.ucr.andthis.edu
7/27/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
david.corfield@tuebingen.mpg.de
7/29/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
baez@math.removethis.ucr.andthis.edu
7/30/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
david.corfield@tuebingen.mpg.de
8/1/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
john baez
7/28/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
Jim Heckman
7/29/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
baez@math.removethis.ucr.andthis.edu
7/31/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
Jim Heckman
8/1/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
Tom Leinster
8/2/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
john baez
7/28/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
tchow@lsa.umich.edu
7/29/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
baez@math.removethis.ucr.andthis.edu
7/30/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
tchow@lsa.umich.edu
8/2/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
john baez
8/7/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
Keith Ramsay
8/8/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
john baez
8/8/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
tchow@lsa.umich.edu
8/24/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
Nik Weaver
7/28/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
David Madore
7/28/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
G. A. Edgar
7/29/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
baez@math.removethis.ucr.andthis.edu
7/30/06
Read graphical representation of epsilon_0 (was: Re: Order-preserving embeddings of ordinals in the real numbers)
David Madore
8/1/06
Read Pictures of infinity
baez@math.removethis.ucr.andthis.edu
8/2/06
Read Re: Pictures of infinity
tony@mantis.co.uk
8/2/06
Read Re: Pictures of infinity
Alec Edgington
8/3/06
Read Re: Pictures of infinity
Dave L. Renfro
7/28/06
Read Re: Order-preserving embeddings of ordinals in the real numbers
Ian A. Mason
7/28/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
Kevin Buzzard
7/29/06
Read Re: This Week's Finds in Mathematical Physics (Week 236)
baez@math.removethis.ucr.andthis.edu

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