Tree-Automatic Well-Founded Trees

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.

Will appear in Logical Methods of Computer Science

References in corpus (1)

• Word Automaticity of Tree Automatic Scattered Linear Orderings Is Decidable

Cited by in corpus (2)

• Structures Without Scattered-Automatic Presentation
• The field of the Reals and the Random Graph are not Finite-Word Ordinal-Automatic