 Solution

ID: past-exam-of-the-model-theory-course-of-the-university-of-oxford/2011/2/a/i/solution

A complete theory is a consistent first-order theory deciding every sentence in its language:

T ⊨ σ or T ⊨ \neg σ for every L -sentence σ .

Equivalently, every two first-order models of

T

are elementarily equivalent. Consistency excludes the vacuous situation in which a first-order theory has no first-order models and entails both alternatives.

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