[FOM] A question on disjunction and numerical existence properties for extensions of HA

[Wojtek Moczydlowski]

   In the article "The Disjunction Property Implies the
Numerical Existence Property" 
(PNAS, August 1, 1975, vol. 72, no. 8, 2877-2878)
Friedman proves the any r.e. extension of HA which satisfies the Disjunction
Property satisfies also Numerical Existence Property. The r.e. assumption is
essential, as there is a \Delta^0_2 theory, obtained by extending HA
with false sentence \phi, which satisfied DP but not NEP.

Is the falseness of \phi essential to construct a counterexample?
In other words, is there a true extension of HA satisfying DP and 
not satisfying NEP?

Wojtek Moczydlowski
Ph. D. student
Computer Science Department
Cornell University