二元本原齐次简单结构
Binary primitive homogeneous simple structures
摘要：
假设M是可数的、二进制的、本原的、齐次的和简单的，因此是基于1的。我们证明了M的完备理论的SU-秩为~1。因此，M是一个随机结构。M是一个随机结构的结论并不成立，如果二进制条件被删除，证明了一般的四面体自由3超图。然而，要证明一般的无四面体3-超图是基于1的需要一些工作（已知它具有其他性质），因为这个概念是根据虚元素定义的。这也是为什么我们也刻画等价关系，这是可定义的，没有参数的背景下，欧米茄范畴结构退化代数闭包。另一个原因是，这样的特征可能是有用的，在未来的研究简单（非二元）均匀结构。
英文摘要：
Suppose that M is countable, binary, primitive, homogeneous, and simple, and hence 1-based. We prove that the SU-rank of the complete theory of M is~1. It follows that M is a random structure. The conclusion that M is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of omega-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
