A simpler axiomatization of the Shelah-Spencer almost sure theories
A simpler axiomatization of the Shelah-Spencer almost sure theories
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Shelah-Spencer 几乎确定理论的更简单公理化
DOI：
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发表时间：
2007
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通讯作者：
M. Laskowski
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文献类型：
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作者：
M. Laskowski
我们给出了稀疏随机图G(n，n−α)的几乎必然理论的显式AE-公理化。在此过程中，我们给出了一种构造相对维度为负但任意小的图的扩张的方法。我们描述了该理论的存在闭模型和局部有限模型，并给出了零维的类型。我们给出了一个有用的分叉刻画，并将图的稳定性和维序性质(DOP)方面的结果推广到任意关系语言。
We give an explicit AE-axiomatization of the almost sure theories of sparse random graphs G(n, n−α) of Shelah-Spencer. In the process we give a method of constructing extensions of graphs whose ‘relative dimension’ is negative, but arbitrarily small. We describe the existentially closed and locally finite models of the theory and produce types of dimension zero. We offer a useful characterization of forking and generalize results about stability and the Dimensional Order Property (DOP) that were known for graphs to arbitrary relational languages.