FOM: RE: Insall's set theory

V. Yu. Shavrukov vys1 at
Tue Sep 19 04:18:12 EDT 2000

Dear Professor Insall,

I am afraid you are not being consistent about your
uppercase/lowercase conventions.

If lower case refers to classes only then in the axiom

>(forall x,y)(thereis z)(forall w)[{[w is in z] iff [(w=x) or (w=y)]}&{[z is
>a set] iff [(x is a set)&(y is a set)]}]

you should probably write  thereis Z, for you do not want to a pair of
proper classes to be a class.

Similarly, in

>(forall f){[f is a function] implies (thereis x)[(x is a class) & {(thereis
>y)[y is in x] & [f(x) is not in x]}]}

you should write  F  for  f.

If lower case refers to collections as well as classes then having a pair
of proper collections appartently contradicts your intention to
keep collection in the same relation to classes as classes are to sets.


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