FOM: Classification of statements
JOE SHIPMAN, BLOOMBERG/ SKILLMAN
JSHIPMAN at bloomberg.net
Tue Apr 21 08:41:54 EDT 1998
Thanks to Harvey for the clarification. When I amended my question to include
known theorems as well as open problems, I should have said "Known theorems are
of course true and hence equivalent to 0=0, so I am referring to the logical
type of the simplest statement to which the theorems are 'trivially equivalent';
here 'trivially equivalent' is imprecise because a precise formulation ought to
involve both base theory and length of proof and I'd rather not get into that
at this point".
I like Harvey's idea of using "constructively equivalent" in place of
"trivially equivalent", though there will still be cases where a long but
constructively valid proof of a theorem makes the issue fuzzy.
When I excluded "logic, fom, and set theory" from my query I meant to exclude
descriptive set theory because of the known connections to large cardinals and
constructibility, not because of any prejudice against such things but because I
wanted to learn something I didn't already know. -- JS
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