Automatic Ordinals

作者：Finkel Olivier^*; Todorcevic Stevo

来源：International Journal of Unconventional Computing, 2013, 9(1-2): 61-70.

• omega-tree-automatic structures
• omega(n)-automatic structures
• ordinals

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 %26gt;= 1 is an integer, are the ordinals smaller than omega(omega n). This strengthens a recent result of Schlicht and Stephan who considered in [21] 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 %26gt;= 1, which was considered in [9], is strict.

• 出版日期2013