Automatic Ordinals
Automatic Ordinals
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自动序数
DOI：
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发表时间：
2012
影响因子：
1.7
通讯作者：
S. Todorcevic
中科院分区：
文献类型：
--
作者：
O. Finkel;S. Todorcevic
证明了内射Ω树自动序数是小于$\omega^{\omega^\omega}$的序数。然后我们证明了内射$\omega^n$-自动序数是小于$\omega^{\omega^n}$的序数，其中$n>0$是一个整数。这加强了最近的结果施利希特和斯蒂芬谁认为在[施利希特-斯蒂芬11]的子类有限字$\omega^n$-自动序数。作为一个副产品，我们得到的层次注入$\omega^n$-自动结构，n>0，这是考虑在[Finkel-Todorcevic 12]，是严格的。
We prove that the injectively omega-tree-automatic ordinals are the ordinals smaller than $\omega^{\omega^\omega}$. Then we show that the injectively $\omega^n$-automatic ordinals, where $n>0$ is an integer, are the ordinals smaller than $\omega^{\omega^n}$. This strengthens a recent result of Schlicht and Stephan who considered in [Schlicht-Stephan11] the subclasses of finite word $\omega^n$-automatic ordinals. As a by-product we obtain that the hierarchy of injectively $\omega^n$-automatic structures, n>0, which was considered in [Finkel-Todorcevic12], is strict.