Martin Huschenbett ; Alexander Kartzow ; Jiamou Liu ; Markus Lohrey - Tree-Automatic Well-Founded Trees

lmcs:721 - Logical Methods in Computer Science, June 25, 2013, Volume 9, Issue 2 -
Tree-Automatic Well-Founded Trees

Authors: Martin Huschenbett ; Alexander Kartzow ; Jiamou Liu ; Markus Lohrey

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.

Volume: Volume 9, Issue 2
Published on: June 25, 2013
Accepted on: June 25, 2015
Submitted on: November 1, 2012
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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