Re: quantifiers

[Iain Alexander <ia@stryx.demon.co.uk>]

re fepni pe mi zo'u:

doi pycy.n

I'm almost certainly misunderstanding _something_ here,
so please tell me what it is.

As a mathematician (sort of) and computer scientist (more or less),
the logical notation I'm familiar with assumes that
consecutive quantifiers are nested.  (Coordinate quantifiers
are not possible in this sort of notation.)

        Ax Ey x broda y

means that for each x there is a y (which is a function of x)
such that (x broda y) holds.

I had naively assumed that this corresponded to an expression
where both quantifiers were in a prenex.

If this is indeed the case, it is not at all obvious why

        3x 3y x broda y

should not also imply that the 'y' quantifier is subordinate
to the 'x' one.

You didn't appear to like Jorge's suggestion that we use multiple
prenexes (prenices?) to denote the nested situation, so I'm not sure

a)      How you represent nested quantifiers
b)      How you decide what's nested and what's absolute if you have
        a mixture of universal, existential and numeric quantifiers
        in a single prenex.

(I'm off to Glasgow for Intersection shortly, so I won't be
contributing for a while.)
--
Iain Alexander                    ia@stryx.demon.co.uk
                    I.Alexander@bra0125.wins.icl.co.uk