Re: Another question on Grothendieck

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

Dear Steve, I was already aware that my statement "only one possible
meaning"? was much too general and I myself speculated (at the time of posting
the msage) about many possible exceptions when literally interpreting my
statement. But I decided to leave it like that. Luckily it was understood as I
meant (private msages).

I clarify to you and to those that may rise similar exceptions:

The Tohoku paper is just plain old classical mathematics (*), and nothing of
the sort of your example is to be found there.

I imagine on the other hand that in your papers you do not let the reader stay
   in the doubt about the meaning of these two possible meanings.


(*) where you can of course point out if some reasoning is constructively
valid (an exceptional example of this is the chapter on field extensions in
the second edition of the classical Van der Waerden book).

e.d.

Steven Vickers wrote:
> Dear Eduardo,
>
> I have written papers that deliberately have two possible meanings: one
> classical point-set and one constructive point-free.
>
> That is to say, the development in terms of points is done under logical
> (geometric) constraints that enable it to be interpreted in topos-valid
> point-free topology (locales), but it can be interpreted directly in
> point-set topology if one accepts classical logic.
>
> I did this for expositional reasons, to help classical topologists
> understand the topological content of what I was doing.
>
> See:
>
>    "Localic completion of generalized metric spaces I"
>    "The connected Vietoris powelocale"
>
> Is this compatible with what you were saying about "only one possible
> meaning"?
>
> Regards,
>
> Steve Vickers.
>

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