FOM: Re: Insall's Set Theory

[Matt Insall]

 Prof. Shavrukov:
 This seems a little bit too radical to me.  By considering  id : V -> V,
 you would get that  V  is a set.


 Matt:
 Sorry, I should have said SET of sets.  You are absolutely right.

 Prof. Shavrukov:
 This denies choice from class many sets, and appears to be in direct
 contradiction with your GCS axiom

 Matt:
 You are right.  I shall need to review our exchanges and your original
 question to see if this malady may be corrected.  In the meantime, the
 following modification seems like a possibility, because it forces x to be
a
 COLLECTION of classes.  This collection may be a collection of class many
 classes.  I seem to recall that that is one way you described what you
 wanted, when you called it ``local'' choice.

 NLCC (revised):
 (thereis x)[(forall w){[w in x] implies [w is a class]} & {(forall f)[f is
a
 function] implies (thereis
 y){(thereis z)[z is in y] & [y is in x] & [f(y) is not in y]}]}



 [PS:  Boy!  I sure wish I took more time working out the details on this
one
 before my first post.  :)]


Dr. Matt Insall
http://www.umr.edu/~insall