论某些均质结构自变群的密集局部有限子群

Pub Date : 2024-07-02 DOI:10.1002/malq.202200060
Gábor Sági
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引用次数: 0

摘要

假设一个可数结构的每个有限部分同构都可以扩展为一个自形。埃文斯问:如果的年龄(有限子结构集)满足赫鲁晓夫斯基的扩展性质,那么其自形群是否真的包含一个密集的局部有限子群?为了研究这个问题,在过去的几十年里,人们引入并研究了赫鲁晓夫斯基外延性质的一个连贯变体。在其他结果中,我们根据相干扩展性质的(新)变体,为密集局部有限子群的存在提供了等价条件。我们还将我们的概念与其他相干外延性质进行了比较。
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On dense, locally finite subgroups of the automorphism group of certain homogeneous structures

Let A $\mathcal {A}$ be a countable structure such that each finite partial isomorphism of it can be extended to an automorphism. Evans asked if the age (set of finite substructures) of A $\mathcal {A}$ satisfies Hrushovski's extension property, then is it true that the automorphism group Aut ( A ) $\operatorname{{\it Aut}}(\mathcal {A})$ of A $\mathcal {A}$ contains a dense, locally finite subgroup? In order to investigate this question, in the previous decades a coherent variant of Hrushovski's extension property has been introduced and studied. Among other results, we provide equivalent conditions for the existence of a dense, locally finite subgroup of Aut ( A ) $\operatorname{{\it Aut}}(\mathcal {A})$ in terms of a (new) variant of the coherent extension property. We also compare our notion with other coherent extension properties.

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