FOM: Finitely axiomatizable theories of sets

Thomas Forster tf at
Mon May 21 20:04:09 EDT 2001

>This isn't what I was looking for.  A "set" in NFU isn't the same thing
as a set in ZFC.  If I was willing to change the meaning of "set" I would
just use VNBG which finitely axiomatizes classes and in which ordinary sets
are definable as those classes which are elements of something.

If it's not what you were looking for, fair enuff.  But it was an answer
to your question. If by `set' you mean `wellfounded set' then you should
say so.  (This is a FOM list not a ZF list, after all)

(Sorry if i sound tetchy - i've just had a screaming match with Adrian
Mathias who is trying to tell me that NF is not set theory. It's one
thing to believe that it's wrong - we are all of us entitled to hold
false beliefs after all, but it's quite another thing to say that it isn't
set theory at all.  I told him that this is a bit like catholics saying
that other christians aren't Christians and i *don't want another
bout of that*!)

     best wishes


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