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In model theory, a discipline within the field of mathematical logic, a tame abstract elementary class is an abstract elementary class (AEC) which satisfies a locality property for types called tameness. Even though it appears implicitly in earlier work of Shelah, tameness as a property of AEC was first isolated by Grossberg and VanDieren,〔.〕 who observed that tame AECs were much easier to handle than general AECs. == Definition == Let ''K'' be an AEC with joint embedding, amalgamation, and no maximal models. Just like in first-order model theory, this implies ''K'' has a universal model-homogeneous monster model . Working inside , we can define a semantic notion of types by specifying that two elements ''a'' and ''b'' have the same type over some base model if there is an automorphism of the monster model sending ''a'' to ''b'' fixing pointwise (note that types can be defined in a similar manner without using a monster model〔, Definition II.1.9.〕). Such types are called Galois types. One can ask for such types to be determined by their restriction on a small domain. This gives rise to the notion of tameness: * An AEC is ''tame'' if there exists a cardinal such that any two distinct Galois types are already distinct on a submodel of their domain of size . When we want to emphasize , we say is -tame. Tame AECs are usually also assumed to satisfy amalgamation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tame abstract elementary class」の詳細全文を読む スポンサード リンク
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