Automatic Ordinals

Abstract : 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.
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Submitted on : Tuesday, May 8, 2012 - 3:34:09 PM
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  • HAL Id : hal-00695443, version 1
  • ARXIV : 1205.1775

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Olivier Finkel, Stevo Todorcevic. Automatic Ordinals. International Journal of Unconventional Computing, Old City Publishing, 2013, 9 (1-2), pp.61-70. ⟨hal-00695443⟩

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