Journal of Mathematical Logic 10 (1):31-43 (2010)

John U. Millar
University of Edinburgh
For countable structure, "Scott rank" provides a measure of internal, model-theoretic complexity. For a computable structure, the Scott rank is at most [Formula: see text]. There are familiar examples of computable structures of various computable ranks, and there is an old example of rank [Formula: see text]. In the present paper, we show that there is a computable structure of Scott rank [Formula: see text]. We give two different constructions. The first starts with an arithmetical example due to Makkai, and codes it into a computable structure. The second re-works Makkai's construction, incorporating an idea of Sacks.
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DOI 10.1142/S0219061310000912
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References found in this work BETA

Generic Copies of Countable Structures.Chris Ash, Julia Knight, Mark Manasse & Theodore Slaman - 1989 - Annals of Pure and Applied Logic 42 (3):195-205.
Pairs of Recursive Structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Effective Model Theory Vs. Recursive Model Theory.John Chisholm - 1990 - Journal of Symbolic Logic 55 (3):1168-1191.

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Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
Strange Structures From Computable Model Theory.Howard Becker - 2017 - Notre Dame Journal of Formal Logic 58 (1):97-105.

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