Re: theorems/problems with lots of quantifiers
From: Jose Juan Mendoza Rodriguez (me_at_privacy.net)
Date: 09/09/04
- Next message: Herman Jurjus: "Re: A question on GIT."
- Previous message: Herman Jurjus: "Re: A question on GIT."
- In reply to: Mitch Harris: "Re: theorems/problems with lots of quantifiers"
- Next in thread: Aatu Koskensilta: "Re: theorems/problems with lots of quantifiers"
- Messages sorted by: [ date ] [ thread ]
Date: Thu, 9 Sep 2004 18:06:28 +0100
>OK, how about the extra rule (which I conveniently forgot to mention)
>that the quantifiers need to -alternate- (because in a logical sense,
>a string of there exists really just collapses to one there exists
>with a possibly nasty encoding of the variables.
>
>--
>Mitch Harris
Hello,
I doubt that you will find more than four alternating quantifiers in
mathematical definitions/theorems. Category theorists like to say that
most sentences in mathematics or computer science can be expressed as
adjunctions between suitable categories, and such sentences take a
sequence of just four alternating quantifiers: forall, exists, forall,
exists.
"... for each object C of C_0, there is an object GC and an arrow
$\varepsilon_C : FGC\rightarrow C$, such that for every object D of D_0
and every arrow $f : FD\rightarrow C$, there is a unique arrow
$\tilde f : D\rightarrow GC$ such that $f = \varepsilon_C \cdot
F \tilde f$."
Here we have a sequence of forall, exists^2, forall^2, exists_unique.
Regards.
José Juan Mendoza Rodríguez
let me=josejuanmr in
let privacy=lycos in
let net=es in
me@privacy.net
- Next message: Herman Jurjus: "Re: A question on GIT."
- Previous message: Herman Jurjus: "Re: A question on GIT."
- In reply to: Mitch Harris: "Re: theorems/problems with lots of quantifiers"
- Next in thread: Aatu Koskensilta: "Re: theorems/problems with lots of quantifiers"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
