[FOM] Foreman's preface to HST
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?
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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