[FOM] The semantics of set theory (Set Theology)

[William Tait]

On Wednesday, October 2, 2002, at 04:58 PM, JoeShipman at aol.com wrote:

>
> Here is a notion of set-theoretic truth that does not require 
> inaccessibles.
>
> Let's expand the language of set theory to include a constant /kappa, 
> and the axiom scheme
>
> phi iff V_/kappa satisfies phi
>
> , for ALL sentences phi in the original language (not including the 
> symbol /kappa)..
>

Joe- maybe its obvious, but what axioms other than this one are there? 
There must be some, since you are assuming that V_\kappa is defined.

Bill Tait