有限图中的秩与预几何

摘要：

有限图模型类的研究是由S. 1969年的希拉。图D是空集上的一组类型，图D的模型类由T的模型组成，这些模型省略了所有不在D中的类型。在这项工作中，我们引入了一个自然的依赖关系的欧米茄稳定的情况下，共享许多形式的分叉属性的模型的子集。这是通过考虑这个框架的秩来实现的，当图D是ω稳定的时，该秩是有界的。我们还可以获得关于这种依赖关系的预几何。依赖关系是秩诱导的自然关系，预几何存在于最小秩类型的实现集合上。最后，这些概念是用来推广的经典结果的模型完全超越一阶理论。事实上，强类比出现了：模型由它们的前几何或它们与它们的前几何的关系决定;然而证明是不同的，因为我们没有紧性。这说明了积极的结果（范畴）以及消极的结果（非同构模型的建设）。

英文摘要：

The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the omega-stable case which share many of the formal properties of forking. This is achieved by considering a rank for this framework which is bounded when the diagram D is omega-stable. We can also obtain pregeometries with respect to this dependence relation. The dependence relation is the natural one induced by the rank, and the pregeometries exist on the set of realizations of types of minimal rank. Finally, these concepts are used to generalize many of the classical results for models of a totally transcendental first-order theory. In fact, strong analogies arise: models are determined by their pregeometries or their relationship with their pregeometries; however the proofs are different, as we do not have compactness. This is illustrated with positive results (categoricity) as well as negative results (construction of nonisomorphic models).

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