FOM: Decidable axioms sets and algorithms in proofs
Torkel Franzen
torkel at sm.luth.se
Tue Dec 16 11:05:18 EST 1997
Neil says:
>Can you make plausible any (necessarily classical) predicament in which one
>knows the set of axioms to be recursive, but one does *not* have such an
>algorithm?
Let the set of axioms of the theory T consist of all true
sentences in the language of PA shorter than k symbols, for some
suitable choice of k. This is a recursively axiomatized theory which
decides your favorite open arithmetical problem, but is
epistemologically useless.
More information about the FOM
mailing list