FOM: epsilon terms and choice

V. Yu. Shavrukov vys1 at
Tue Sep 19 01:31:45 EDT 2000

Dear Professor Insall,

I am having difficulty making sense of your set theory T.

>(forall x)(forall y)[(x is in y) iff (x is a class)]
>(forall x)(forall y){[(x is in y)&(y is a class)] iff (x is a set)}

both these axioms look very strange to me.
I wonder if they express what you meant to express.
It might have been better if you spelt them out in words.

It would also help if you explained what the relation of
'classes' to the rest of the entities in T's universe is.
Is everything a class?  Is the universe partitioned into
classes and sets?  Should one read 'class' as proper class?

>(forall X_1,...,X_n)(thereis Y)(forall x)[x is in Y iff phi(X_1,...,X_n,x)]

any restrictions on phi?

>(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]}]}

This suggests to me that you are willing to allow some classes
to be elements of other classes.  Is this what really you want to do?


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