Model-theoretic complexity of automatic structures
Author(s)
Khoussainov, Bakhadyr; Minnes, Mia
DownloadKhoussainov-2009-Model-theoretic comp.pdf (686.0Kb)
PUBLISHER_POLICY
Publisher Policy
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Terms of use
Metadata
Show full item recordAbstract
We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor–Bendixson ranks (of trees). We prove the following results: (1) The ordinal height of any automatic well-founded partial order is bounded by ω[superscript ω]. (2) The ordinal heights of automatic well-founded relations are unbounded below ω[subscript 1 superscript CK], the first non-computable ordinal. (3) For any computable ordinal α, there is an automatic structure of Scott rank at least αα. Moreover, there are automatic structures of Scott rank ω[subscript 1 superscript CK],ω[subscript 1 superscript CK] +1. (4) For any computable ordinal α, there is an automatic successor tree of Cantor–Bendixson rank α.
Date issued
2009-08Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Annals of Pure and Applied Logic
Publisher
Elsevier
Citation
Khoussainov, Bakhadyr, and Mia Minnes. “Model-Theoretic Complexity of Automatic Structures.” Annals of Pure and Applied Logic 161, no. 3 (December 2009): 416–426. © 2009 Elsevier B.V.
Version: Final published version
ISSN
01680072