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 | 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 [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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