Abstract:
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 ( 2003) is best possible for trivial strongly minimal theories in terms of computable model theory. We conclude with some remarks about axiomatizability.