Re: Cantor's definition of set

On Oct 27, 10:44?pm, G. Frege <nomail@invalid> wrote:
On Sat, 27 Oct 2007 13:51:25 +0200, Jan Burse <janbu...@xxxxxxxxxxx>
wrote:



forall x (
Set(x) -> forall y(
Set(y) -> forall z((z in x <-> z in y) -> x=y)))

Again, I'd rather write

Ax(set(x) -> Ay(set(y) -> (Az(z e x <-> z e y) -> x = y))).

Oops, yes sure.

In addition, see Chris Menzel's comments. This is just formulated in
good old standard FOPL (with identity). "set" could be defined the
following way (for example):

set(x) :<-> Ey(y e x) v x = 0.

(Given that 0 is a primitive of our system.)

So a /set/ is just an object with elements, or the empty set. (I'm
thinking of a variant of ZFC with urelements here; no proper classes.)

F.

--

E-mail: info<at>simple-line<dot>de
-----------

So a /set/ is just an object with elements, or the empty set. (I'm
thinking of a variant of ZFC with urelements here; no proper classes.)

Yes. But you should give some examples. Give us an example of a set
that is an object, such as a set of cutlery. You will no doubt want to
phrase this in some object language such as a,b, etc. rather than an
everyday object.

.

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