[FOM] Structure of nonstandard models of PA

[Roger Bishop Jones]

It has been observed that all countable non-standard
models of PA have the same order-type.

Clearly, however, they are not all equivalent, since
they differ in which denials of consistency claims
they satisfy, giving at least countably many
countable non-standard models of PA which are not
elementarily equivalent.

Is there anything published on the structure of
non-standard models of PA which illuminates the
differences between the countable models?

Roger Jones