Re: Cantor's definition of set

On Sat, 27 Oct 2007 14:32:47 +0200, Jan Burse <janburse@xxxxxxxxxxx> said:
...
Sets are nameless. This follows from the axiom of "extensionality".
This axiom exactly says that sets do not have names.

Surely it does not. It says nothing about names whatsoever.

There are some nonstandard set theories, AFA and so on, that work
with so called decorated sets.

You mean decorated graphs.

You can view a decoration as a name that has a set attached.

Perhaps you can, but it would be a mistake. :-) A decoration is a
certain type of function from the nodes of an "accessible pointed graph"
to sets (or, if you like, sets and urelements).

http://inconsistent.typepad.com/home/2006/07/which-sets-are-.html

But this is rather a device to depict these nonstandard sets,
that do not follow the well founded axiom. But still they follow
also the extensionality axiom!

Sure thing. Extensionality and foundation are independent of one
another.

.