Tree-Automatic Well-Founded Trees

Martin Huschenbett, Alexander Kartzow, Jiamou Liu, Markus Lohrey, Anuj Dawar
2013 Logical Methods in Computer Science  
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
more » ... tree-automatic well-founded trees is complete for level Delta^0_omega^omega of the hyperarithmetical hierarchy with respect to Turing-reductions.
doi:10.2168/lmcs-9(2:10)2013 fatcat:q5qbkycnzrdvrl6mlexjfcif4u