FOM: Classical over Intuitionistic

Joseph Shoenfield jrs at
Thu Oct 15 11:38:32 EDT 1998

     I am slightly puzzled by the statement:
     >PA is conservative over HA for pi-0-2 sentneces.
     I presume this depends on only allowing plus and times as non-
logical constants.   If one allows Kleene's T-predicate, a counter-
example is (forall x)(A(x) or not-A(x)) where A(x) is a sigma-0-1
formula which defines a non-recursive set.

More information about the FOM mailing list