|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||Abstract:||
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  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 , is strict.
|Keywords:||ω-Tree-Automatic Structures; | ω -Automatic Structures n | Ordinals||Publisher:||Old City Publishing|
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