维数、拟阵和一阶结构的稠密对
Dimension, matroids, and dense pairs of first-order structures
摘要：
一个结构M是预几何的，如果它的代数闭包是在所有M'中与M基本等价的预几何.我们定义了一个推广：结构与存在拟阵。主要的例子是超稳定群的U-秩Ω和d-最小扩展领域的权力。扩展一个域的前几何结构的超积，虽然一般不是前几何的，但确实有唯一的存在拟阵。推广以前的结果，范登德里斯，我们定义了密集的基本对结构扩展领域和存在拟阵，我们表明，相应的理论有自然的完成，其模型也有一个独特的存在拟阵。我们将上述结果推广到稠密结构元组。
英文摘要：
A structure M is pregeometric if the algebraic closure is a pregeometry in all M' elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of U-rank a power of omega and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding a field, while not pregeometric in general, do have an unique existential matroid. Generalising previous results by van den Dries, we define dense elementary pairs of structures expanding a field and with an existential matroid, and we show that the corresponding theories have natural completions, whose models also have a unique existential matroid. We extend the above result to dense tuples of structures.
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