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arXiv · 1201.5495

Tree-Automatic Well-Founded Trees

Martin Huschenbett·Alexander Kartzow·Jiamou Liu·Markus Lohrey
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Abstract

We investigate tree-automatic well-founded trees. Using Delhomme's decomposition technique for tree-automatic structures, we show that the (ordinal) rank of a tree-automatic well-founded tree is strictly below omega^omega. Moreover, we make a step towards proving that the ranks of tree-automatic well-founded partial orders are bounded by omega^omega^omega: we prove this bound for what we call upwards linear partial orders. As an application of our result, we show that the isomorphism problem for tree-automatic well-founded trees is complete for level Delta^0_{omega^omega} of the hyperarithmetical hierarchy with respect to Turing-reductions.

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Martin Huschenbett, Alexander Kartzow, Jiamou Liu, Markus Lohrey. 2013-06-24. Tree-Automatic Well-Founded Trees. https://doi.org/10.2168/lmcs-9(2%3A10)2013

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