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Topic: A canonical form for small ordinals
Replies: 12   Last Post: Jan 19, 2014 2:35 PM

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ross.finlayson@gmail.com

Posts: 1,220
Registered: 2/15/09
Re: A canonical form for small ordinals
Posted: Jan 19, 2014 2:35 PM
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On 1/19/2014 2:37 AM, Paul wrote:
> On Saturday, January 18, 2014 11:48:13 PM UTC, Ross A. Finlayson wrote:
>

>>
>>
>> William, Elliott, quasi, or Dr. Quasi or whatever it is these days,
>>
>> please explain what you see as the significance of the result you
>>
>> have proven.

>
> Ross,
>
> I think the answer to that question is rather obvious. It occurred as an unproved assertion in a paper I was reading. I requested help in understanding why this was true and others on the thread (including quasi and William Elliot but others made useful comments, too) made contributions with the (successful) aim of helping me understand what I was reading.
>
> Paul Epstein
>


Thanks Paul,

The reason I asked is because of the machinery here of canonical
forms for "small" ordinals less than epsilon_0 or omega_1, as it
were, which is _all of them that can be named_. The result
establishes that for each name-able/constructible ordinal, that
there's a mapping between it and any other: and here a normal form.
If that's obvious, I'm wondering if you read into the result, from
being able to map any larger small ordinal onto a small ordinal in a
normal way, is that uniqueness is satisfied, of the form for the
ordinals.

https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)

Thanks for your reply.

Regards, Ross Finlayson





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