The Rank of Tree-Automatic Linear Orderings

  title={The Rank of Tree-Automatic Linear Orderings},
  author={Martin Huschenbett},
A tree-automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. The finite condensation rank (FC-rank) of a linear ordering measures how far it is away from being dense. We prove that the FC-rank of every tree-automatic linear ordering is below omega^omega. This generalises Delhomme's result that each tree-automatic ordinal is less than omega^omega^omega… Expand

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