#### Journal Title

Proceedings of the American Mathematical Society

#### Publication Date

2-24-2003

#### Abstract

We prove that if *M* is any model of a trivial, strongly minimal theory, then the elementary diagram Th(*M _{M}*) is a model complete

*L*-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 Σ

_{M}^{0}

_{5}.

#### Subjects

Mathematical models

#### Citation: Pilot Scholars Version (Modified MLA Style)

Goncharov, Sergey S.; Harizanov, Valentina S.; Laskowski, Michael C.; Lempp, Steffen; Solomon, Reed; and Mccoy, Charles F. D., "Trivial, Strongly Minimal Theories Are Model Complete After Naming Constants" (2003). *Mathematics Faculty Publications and Presentations.* Paper 7.

http://pilotscholars.up.edu/mth_facpubs/7

#### Peer-Reviewed

Yes

#### Document Type

Journal Article

## Publication Information

Proceedings of the American Mathematical Society, 2003, Vol. 131, No. 12, pp. 3901-3912

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