Model-companions and definability in existentially complete structures
Model-companions and definability in existentially complete structures
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存在完整结构中的模型伴生和可定义性
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
W. Wheeler
中科院分区：
文献类型：
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作者：
W. Wheeler
模型伴侣和存在完备结构的理论都是回顾和进一步发展。复习从A开始。罗宾逊的工作在50年代，并继续通过可定义的二阶结构的存在完整的群体。新的结果包括一个模型伴侣的存在的必要和充分条件，在一般的基本性质的可定义性。本文的主要定理给出了有限表示泛理论存在伴模的充要条件和合并性质。这个结果推广了P. Eklof和G. Sabbagh证明了R-模理论有模型完备性当且仅当R是凝聚的。
The theory of model-companions and existentially complete structures is both reviewed and developed further. The review begins with A. Robinson’s work in the fifties and continues through the definability of second order structures in existentially complete groups. New results include necessary and sufficient conditions for the existence of a model-companion in terms of the definability of general elementary properties. The main theorem of the paper gives necessary and sufficient conditions for the existence of a model-companion for universal theories with finite presentations and the amalgamation property. This result generalizes the result of P. Eklof and G. Sabbagh that the theory ofR-modules has a model-completion if and only ifR is coherent.