The Small Index Property for ω‐Stable (ω‐Categorical Structures and for the Random Graph
The Small Index Property for ω‐Stable (ω‐Categorical Structures and for the Random Graph
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ω-稳定（ω-分类结构）和随机图的小指数性质
DOI：
10.1112/jlms/s2-48.2.204
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发表时间：
1993
影响因子：
1.2
通讯作者：
S. Shelah
中科院分区：
文献类型：
--
作者：
W. Hodges;I. Hodkinson;D. Lascar;S. Shelah
给出了一个可数结构具有小指数性质的一个判据，该判据涉及许多自同构类属序列的存在。我们用它来证明：(I)任意a&>-稳定的上范畴结构，以及(Ii)随机图具有小指数性质。我们还证明了这种结构的自同构群不是真子群的可数链的并。
We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any a>-stable co-categorical structure, and (ii) the random graph have the small index property. We also show that the automorphism group of such a structure is not the union of a countable chain of proper subgroups.