[FOM] Flexible Predicates and End Extensions

[Ali Enayat]

In an earlier posting (June 2), I mentioned a theorem concerning end
extensions of models of PA, provable using flexible r.e. sets, whose
statement requires M to satisfy not only PA, but PA+Con(PA), more
precisely:

Theorem. There is an r.e. set W_e such that:

(a) PA + Con(PA) proves "W_e is empty", and

(b) If M is any model of PA + Con(PA), and S is a subset of M that is
finite in the sense of M (i.e., M can be coded by an element of M via base
2 coding), there is an end extenion N of M satisfying PA such that W_e, as
computed in N, is precisely S.

Regards,

Ali Enayat