[Python-3000] sets in P3K?

[Gareth McCaughan]

On Tuesday 2006-04-25 20:20, Tim Peters wrote:

> Now you can only use a set if you can prove it exists, and one way to
> prove a set exists is via what was once called the Axiom of
> Comprehsion (but seems to be called the Axiom of Subsets more often
> these days).  That says that if you have a set S, then for any
> one-place predicate P, {x ? S | P(x)} exists.  So you can still make
> up any predicate you like, but you can only use it to "separate out"
> (why it's also sometimes, but I think rarely, called the Axiom of
> Separation) the satisfiyng elements from another set.

<irrelevant math-geekery>

When I was last studying this stuff, "Comprehension" meant the
unrestricted schema (which yields inconsistency with the rest
of the ZF axioms) and "Separation" meant the restricted one.
I've not heard "axiom of subsets", which I quite like (except
that, like comprehension and separation, it's really an axiom
schema, not a single axiom) despite the possibility of confusing
it with the power set axiom.

The Web of a Million Lies suggests that maybe terminological
fashions have changed a bit in this area over the last decade
or so.

</>

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g