FOM: Finitely axiomatizable theories of sets

Thomas Forster tf at
Mon May 21 13:49:14 EDT 2001

> are there interes
ting finitely axiomatizable theories of sets that allow one to do all or most
of "ordinary mathematics"?

Yes - lots of extensions of NFU for example.

On anotherr point raised by Shipman: the finite axiomatisability or
otherwise of Zermelo.  I would like some elucidation of the reasons
Friedman gives for the negative answer.  One reason for this is the
my friend and DoktorVater Adrian Mathias spent some time getting a
negative answer  (he dug back to some work of Montague's i seem to 
recall) and he's no mug so even assuming that what Harvey says is
true i doubt if the details are straightforward.  If Adrian is tuned
in (Reunion is the antpodes of Irvine so at this precise minute he's
probably tucked up in bed) he will probably have something to say.

Finally a remark of the late Jean Coret's that may be relevant:
additing stratified axioms to Zermelo will never give a consisten
extension of ZFC.

   Thomas Forster

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