论文标题
随机POSET的通用自动形态的结构
The structure of generic automorphisms of the random poset
论文作者
论文摘要
我们检查了随机Poset的通用自动形态的属性，其目的是明确表征它们。我们将每种自动形态与辅助一阶结构相关联，该结构由配备无限二进制关系序列的随机POSET组成，该二进制关系编码自动形态的作用。然后，我们根据该结构的性质明确表征通用自动形态。此类典型的两个显着特性是超血糖性，并且是该语言中某些有限结构的普遍性。由于这种辅助结构似乎是新的，因此我们还解决了一些模型理论问题。特别是，与许多已知的有限语言中许多已知的超双重固醇结构相比，这种结构均未饱和，其理论也不是$ω$分类的也不是量化量子。我们还检查轨道 - 轨道的订单凸壳 - 以及它们在描述自动形态的使用。特别是，我们在轨道空间中介绍并使用新订单。
We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an infinite sequence of binary relations which encode the action of the automorphism. We then explicitly characterize generic automorphisms in terms of properties of this structure. Two notable such properties are ultrahomogeneity, and universality for a certain class of finite structures in this language. As this auxiliary structure seems to be new, we also address some model-theoretic questions. In particular, this structure fails to be saturated, and its theory neither is $ω$-categorical nor admits quantifier-elimination, in contrast to many known ultrahomogeneous structures in finite languages. We also examine orbitals -- order-convex hulls of orbits -- and their use in describing automorphisms. In particular, we introduce and use new orders on the space of orbitals.
