FOM: Nonstandard models of N

[Dave Marker]

Another positive result is obtained by combining a Henkin argument
with the Jockusch-Soare low basis theorem to produce a low
nonstandard model of arithmetic (i.e. the jumps of + and * are only
0').

The result that there is no arithmetic nonstandard model of true
arithmetic is due to Feferman.

I believe that Julia Knight has a survey article on this subject in
the recently published Handbook of Computability Theory.

Dave Marker