Model theoretic dynamics in Galois fashion
Model theoretic dynamics in Galois fashion
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伽罗瓦时尚的理论动力学模型
DOI：
10.1016/j.apal.2019.02.002
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
D. Hoffmann
中科院分区：
文献类型：
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作者：
D. Hoffmann
我们固定了一个稳定理论的Monster模型D，研究了D的子结构，这些子结构在赋固定群G的作用的子结构类内存在闭，我们把它们描述为D的PAC子结构，得到了与Galois理论有关的结果。假设这些存在闭子结构的类是初等的，我们证明了，在有界模型的假设下，它的理论是简单的，并且省略了直到某些存在公式的量词。此外，这一理论对有限集合进行了编码，并允许对想象进行几何消除，但并不总是对想象进行弱消除。
We fix a monster model D of some stable theory and investigate substructures of D which are existentially closed within the class of substructures equipped with an action of a fixed group G. We describe them as PAC substructures of D and obtain results related to Galois theory. Assuming that the class of these existentially closed substructures is elementary, we show that, under the assumption of having bounded models, its theory is simple and eliminates quantifiers up to some existential formulas. Moreover, this theory codes finite sets and allows a geometric elimination of imaginaries, but not always a weak elimination of imaginaries.