Since the theorems of (PA + "there is a nonstandard number") are recursively enumerable, by the
<br>
[Low Basis Theorem](http://en.wikipedia.org/wiki/Low_basis_theorem), [WKL0](http://en.wikipedia.org/wiki/Reverse_mathematics#Weak_K.C3.B6nig.27s_lemma_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][1] to
<br>
[this question](https://mathoverflow.net/questions/29550/completeness-easiest-hardest-problems), I wonder "how easy" such a model could be to compute.

<br>

Can a low nonstandard model of PA be:
<br>
a) minimal
<br>
b) computably dominated
<br>
c) K-trivial
<br>
?

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


  [1]: https://mathoverflow.net/questions/29550/completeness-easiest-hardest-problems/35566#35566