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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?

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# Turing degrees of nonstandard models of PA

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?