We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model \(\mathcal {A}\) of a computably enumerable, model complete theory, the entire elementary diagram \(E(\mathcal {A})\) must be decidable. We prove that indeed a c.e. theory T is model complete if and only if there is a uniform procedure that succeeds in deciding \(E(\mathcal {A})\) from the atomic diagram \(\varDelta (\mathcal {A})\) for all countable models \(\mathcal {A}\) of T. Moreover, if every presentation of a single isomorphism type \(\mathcal {A}\) has this property of relative decidability, then there must be a procedure with succeeds uniformly for all presentations of an expansion \((\mathcal {A},\mathbf {a})\) by finitely many new constants.

我们研究了一种理论的模型完整性对于该理论模型的表示有效性的影响。立即对于可计算的，模型完全理论的可计算模型\（\ mathcal {A} \），整个基本图\（E（\ mathcal {A}）\）必须是可确定的。我们证明，仅当有一个统一的过程成功地从原子图\（\ varDelta（\ mathcal {A} ）决定\（E（\ mathcal {A}）\）时，ce理论T的模型才是完整的。 ）\）的所有可数模型\（\ mathcal {A} \）的Ť。此外，如果每个表示的同构类型都是\（\ mathcal {A} \）具有相对可决定性的特性，那么必须有一个过程，通过有限的许多新常量，对扩展\（（\ mathcal {A}，\ mathbf {a}）\）的所有表示形式都具有统一的成功。