On countable stable structures which are homogeneous for a finite relational language
On countable stable structures which are homogeneous for a finite relational language
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关于有限关系语言同质的可数稳定结构
DOI：
10.1007/bf02760647
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发表时间：
1984
影响因子：
1
通讯作者：
A. Lachlan
中科院分区：
文献类型：
--
作者：
A. Lachlan
设L是一种有限关系语言，H(L)表示所有可数结构的类，这些结构对于L来说在Fraissé意义上是稳定且齐次的。按照惯例，可数包括有限的，任何有限的结构都是稳定的。引入了秩函数 r :H(L) →ω 以及 H(L) 中结构的维数概念。定义了缩小结构的规范方法，以减少其尺寸。论文的主要结果是，anyM ∈H(L) 可以收缩为 M′ εH(L),M′ ⊆M，使得 |M′|以 r(M) 为界，且 M 在 M' 上的同构类型由 M 的维数唯一确定。对于r<ω，我们推导出H(L, r)，即所有M ∈H(L) 且r(M)≤r 的类，是有限数量的类的并集，每个类中结构的同构类型完全由其维度决定。
LetL be a finite relational language andH(L) denote the class of all countable structures which are stable and homogeneous forL in the sense of Fraissé. By convention countable includes finite and any finite structure is stable. A rank functionr :H(L) →ω is introduced and also a notion of dimension for structures inH(L). A canonical way of shrinking structures is defined which reduces their dimensions. The main result of the paper is that anyM ∈H(L) can be shrunk toM′ ∈H(L),M′ ⊆M, such that |M′| is bounded in terms ofr(M), and the isomorphism type ofM overM′ is uniquely determined by the dimensions ofM. Forr<ω we deduce thatH(L, r), the class of allM ∈H(L) withr(M)≦r, is the union of a finite number of classes within each of which the isomorphism type of a structure is completely determined by its dimensions.