[FOM] Field with one element, part I, correcting a correction

[Colin McLarty]

Actually I was wrong to say I was wrong in Tue, Jun 21, 2016 at 8:48 AM,
Colin McLarty <colin.mclarty at case.edu> wrote:

> From this point of view F1 should be a subfield of every finite field,
>> which
>> > is impossible with the standard definition of field.
>>
>> [Omitting sensible reply from Harvey]
>
>
> This is my mistake.  The snippet quoted from me should have said the
> spectrum of F1 is a *quotient* of each finite field.
>

In fact my original, as quoted, is correct.  At least two of the original
motivations for F1 would make it a subfield of each finite field, and a
subfield of Z.  One of those is that F1 is the (conventionally
non-existent) special case of a field with p^n elements where p is prime
and n=0.

Anyway, I still conclude that Harvey's suggestion is an interesting
contrast to the geometric  motivations of Tits and others.  And I still
plan to send in a part II on some approaches to the Tits idea.

best, Colin
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20160621/ad9d37d1/attachment-0001.html>