Trivial, Strongly Minimal Theories Are Model Complete After Naming Constants

Sergey S. Goncharov
Valentina S. Harizanov
Michael C. Laskowski
Steffen Lempp
Charles F. D. McCoy, University of Portland

Abstract

We prove that if M is any model of a trivial, strongly minimal theory, then the elementary diagram Th(MM) is a model complete LM-theory. We conclude that all countable models of a trivial, strongly minimal theory with at least one computable model are 0"-decidable, and that the spectrum of computable models of any trivial, strongly minimal theory is EO.