Authors: Finkel, Olivier
Todorčević, Stevo 
Title: Automatic ordinals
Journal: International Journal of Unconventional Computing
Volume: 9
Issue: 1-2
First page: 61
Last page: 70
Issue Date: 16-Apr-2013
Rank: M23
ISSN: 1548-7199
We prove that the injectively ω-tree-automatic ordinals are the ordinals smaller than ωωω . Then we show that the injectively ωn -automatic ordinals, where n ≥ 1 is an integer, are the ordinals smaller than ωωn . This strengthens a recent result of Schlicht and Stephan who considered in [21] the subclasses of finite word ωn -automatic ordinals. As a by-product we obtain that the hierarchy of injectively ωn -automatic structures, n ≥ 1, which was considered in [9], is strict.
Keywords: ω-Tree-Automatic Structures; | ω -Automatic Structures n | Ordinals
Publisher: Old City Publishing

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