eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2013-02-26
586
597
10.4230/LIPIcs.STACS.2013.586
article
The Rank of Tree-Automatic Linear Orderings
Huschenbett, Martin
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 Delhommé'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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol020-stacs2013/LIPIcs.STACS.2013.586/LIPIcs.STACS.2013.586.pdf
tree-automatic structures
linear orderings
finite condensation rank
computable model theory