The Rank of Tree-Automatic Linear Orderings
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 DelhommÃ©'s result that each tree-automatic ordinal is less than omega^omega^omega. Furthermore, we show an analogue for tree-automatic linear orderings where the branching complexity of the trees involved is bounded.
tree-automatic structures
linear orderings
finite condensation rank
computable model theory
586-597
Regular Paper
Martin
Huschenbett
Martin Huschenbett
10.4230/LIPIcs.STACS.2013.586
Creative Commons Attribution-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nd/3.0/legalcode