Re: The Dedekind Snap

On Dec 16, 11:39 am, Herbert Newman <nomail@invalid> wrote:
MoeBlee wrote:

Note that in this case "0" is a primitive.

No, it is defined.

We prove: E!xAy ~yex.

Then define: 0=x <-> Ay ~yex.

c is a class <-> (Ex xec v c=0)

Well, no proper classes in Z (sic!) set theories! ;-)

Yes, so?

And why the 'sic'?

Hence:

  y is a set <-> (Ex xey v y=0)

A very reasonable definition imho: Something is a set if it has some
elements,  o r  (otherwise) is the empty set (sic!).

That's fine, except my definition is "portable" to class theories such
as NBG. My definition works also in NBG in accord with the notion of
set in that theory.

MoeBlee


.

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