FOM: completeness theorem for stratification?

[Stephen G Simpson]

This is a belated comment on Thomas Forster's FOM posting of March 8,
2000.  Regrettably, I have been too busy the last few months to
participate much in FOM.

On March 7 I asked whether there is a clear and convincing description
of the NF view of sets.  On March 8 Forster responded:

 > Inasfar as there is a story available at the moment, i think it is the
 > idea of stratfication, which is a lot more sensible than one realises.
 > There is a completeness theorem for stratification, to the effect that
 > it's an invariance property.  But we've been over this material before
 > on this list, so presumably this is not what Steve has in mind.

I'm sorry, I don't understand.  Stratification still seems highly
nonintuitive to me.  The problem I have is that, although the formulas
are untyped, one must assign types in order to use them.  Thomas,
could you please explain?

What is the completeness theorem for stratification, and in what sense
is it an invariance property?  Maybe we have been over this ground
earlier on FOM, but I don't remember it.  Could you please give a
reference to a relevant FOM posting?  I am not finding it with an FOM
search (on the FOM home page, www.math.psu.edu/simpson/fom/) using
``invariance'' as the search string.

-- Steve