On the computability-theoretic complexity of trivial, strongly minimal models

Bakhadyr M. Khoussainov, Michael C. Laskowski, Steffen Lempp, Reed Solomon
2007 Proceedings of the American Mathematical Society  
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 0 . This result shows that the result of Goncharov/Harizanov/Laskowski/Lempp/McCoy [GHLLM03] is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks about axiomatizability.
doi:10.1090/s0002-9939-07-08865-x fatcat:cuml346dkfg37hitqrlohzyx6u