SUO: Re: IFF LOT Glossary
----- Original Message -----
From: "Jon Awbrey" <jawbrey@att.net>
To: "Robert E. Kent" <rekent@ontologos.org>
Cc: "SUO" <standard-upper-ontology@ieee.org>
Sent: Sunday, July 06, 2003 6:25 AM
Subject: Re: IFF LOT Glossary
> o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
>
> Robert E. Kent wrote:
> >
> > Jon,
> >
> > The base functor could also be called the underlying language functor.
>
> Okay, that helps a little. So it does begin to sound like a forgetful
functor,
> for example, the functor ||...|| : Groups -> Sets, G ~> ||G||, that gives
you
> the underlying set of a group.
It is exactly a forgetful functor in the same mannor.
.> But now I need to get a bit clearer as to how you see
> there being 'the' underlying language of a theory.
>
> First question. Do you really mean any theory,
> or just the sort of a theory that constitutes
> a "finite axiom set" (FAS)?
I mean a theory as in (page 12 of Chang & Keisler, Model Theory 1977).
I have made no use (so far!) of finiteness. In fact, I have gone out of my
way to find the exactly correct generality, avoiding finiteness and natural
numbers objects (NNO). Eventually I know that I will need to have an NNO,
but then we become more specific, heading toward a topos.
Robert E. Kent
rekent@ontologos.org