Computer Science – Logic in Computer Science
Scientific paper
2012-04-13
Computer Science
Logic in Computer Science
20 pages, 3 figures
Scientific paper
We generalise Delhomm\'e's result that each tree-automatic ordinal is strictly below \omega^\omega^\omega{} by showing that any tree-automatic linear ordering has FC-rank strictly below \omega^\omega. We further investigate a restricted form of tree-automaticity and prove that every linear ordering which admits a tree-automatic presentation of branching complexity at most k has FC-rank strictly below \omega^k.
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