FOM: Intuitionism (Tait)
Axiomize@aol.com
Axiomize at aol.com
Mon Jun 17 09:29:23 EDT 2002
Subj:RE: FOM: Intuitionism (Tait)
Date:6/14/02 10:01:39 AM Eastern Daylight Time
From:kru at voll.math.msu.su
To:fom at math.psu.edu
Sent from the Internet (Details)
>> Since (Proposition 3.23, p. 131, Elliott Mendelson, 1964, Introduction to
Mathematical Logic, Van Nostrand, New York), then I would expect as much.
>> Charlie Volkstorf
> Thank you. Now I see that the corresponding proof predicate can be
constructed via Fixed Point Theorem but I don't see any direct ("suitable for
programming") construction of a decidable (\Delta_{1}-formula) proof
predicate with the property Prf(n,F)->Prf(n,Prf(n,F)).
> Vladimir N. Krupski
Must the proof of P be the same as the proof that this proof proves P? As a
proof proves only one sentence (if we defined it to include corollaries, then
Prf would no longer be recursive, but only recursively enumerable), then F
would have to coincide with Prf(n,F).
Would a recursive f such that Prf(n,F)->Prf(f(n),Prf(n,F)) be helpful?
(Shall we make the implication two-way?) Or perhaps combine them into
Prf(n,F^Prf(n,F))?
Charlie Volkstorf
M-Tools
Cambridge, MA
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