On the computability-theoretic complexity of trivial, strongly minimal models
Bakhadyr Khoussainov, Michael Chris Laskowski, Steffen Lempp, Reed Solomon · Proceedings of the American Mathematical Society · 2007
We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes $\boldsymbol {0}''$. This result shows that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy (2003) is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks about axiomatizability.