Since the theorems of (PA + "there is a nonstandard number") are recursively enumerable, by the

Low Basis Theorem, WKL0's proof of the completeness theorem gives a nonstandard model of PA of [low degree](http://en.wikipedia.org/wiki/Low_(computability). After seeing Adam Day's answer to

this question, I wonder "how easy" such a model could be to compute.

Can a low nonstandard model of PA be:

a) minimal

b) computably dominated

c) K-trivial

?

If it can be more than one of those, which can it be simultaneously?