[FOM] Foreman's preface to HST

joeshipman@aol.com joeshipman at aol.com
Thu Apr 29 19:48:41 EDT 2010

By "easily" I mean that it is easy to see that the arguments can in 
principle be written in FOL+ZFC, so that no other "foundation" is 
necessary. Two examples where it is not necessarily easy:

1) Category theory was used in a way not obviously reducible to ZFC, 
until the Grothendieck Universes axiom was shown to suffice -- and this 
is still not ZFC but ZFC plus a large cardinal axiom. Thus, many 
results of algebraic geometry have not officially been shown to be 
theorems of ZFC. I was wondering if this was the only example.

2) NF is not reducible to ZFC since we have no consistency proof; 
however I am not aware of any mathematical researcher who uses NF as 
his base theory AND uses techniques that cannot easily be seen to be 
reinterpretable as ZFC arguments. Can Forster, Holmes, or Enayat 
suggest something here?

-- JS

-----Original Message-----
From: A. Mani <a_mani_sc_gs at yahoo.co.in>

What exactly do you mean by 'easily'?
Plenty of Mathematics would look fairly terrible if written in FOL+ZFC.

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