[FOM] Re: The width of V

[Roger Bishop Jones]

On Tuesday 08 July 2003  7:25 pm, Eric Steinhart wrote:
> From: Roger Bishop Jones <<rbj at rbjones.com>
>
> >Can anyone point me to work on axioms which
> >
> >are intended to make V as fat as possible?
>
> It would seem that the plain old power set axiom makes V as
> wide as possible, if you take V[n+1] to be the power set of
> V[n] for any ordinal n.

The power set axiom says nothing about what subsets there
are, it just says that such subsets as there are, are
the members of the power set.

The axioms which most explicitly attempt to say that
all the subsets exist are found in the separation schema.
Unfortunately this affirms the existence only of those
subsets whose extension can be expressed by a first order
formula.

Roger Jones