FOM: Why Friedman's result is a big improvement

Torkel Franzen torkel at
Wed Mar 25 02:07:39 EST 1998

  Joe Shipman says:

  >Franzen has argued that the Diophantine equations representing
  >ZFC-provability are already independent combinatorial statements of a
  >simple type and questions how much of an improvement Harvey's
  >independent statements about finite trees and insertion rules can be.

  It seems that you've lost sight of the context of my invocation of
Diophantine statements, which was quite specific: Neil Tennant's
view that Friedman's (A) is a statement which, if true, should be true
for simple reasons. This, he has explained, is what he finds
most striking about the equivalence (A)<=>(B). Hence my reference
to Diophantine equivalents of (B). What is the relevant difference
between Diophantine statements and (A), from the point of view of
the idea that (A), if true, should be true for simple reasons? An
answer to this question would be helpful in the further examination
of that idea.

Torkel Franzen

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