Journal of Symbolic Logic 71 (1):283 - 298 (2006)

Makkai [10] produced an arithmetical structure of Scott rank $\omega _{1}^{\mathit{CK}}$. In [9]. Makkai's example is made computable. Here we show that there are computable trees of Scott rank $\omega _{1}^{\mathit{CK}}$. We introduce a notion of "rank homogeneity". In rank homogeneous trees, orbits of tuples can be understood relatively easily. By using these trees, we avoid the need to pass to the more complicated "group trees" of [10] and [9]. Using the same kind of trees, we obtain one of rank $\omega _{1}^{\mathit{CK}}$ that is "strongly computably approximable". We also develop some technology that may yield further results of this kind
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DOI 10.2178/jsl/1140641175
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References found in this work BETA

Pairs of Recursive Structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Ramified Systems.C. J. Ash & J. F. Knight - 1994 - Annals of Pure and Applied Logic 70 (3):205-221.
Scott Sentences and Admissible Sets.Mark Nadel - 1974 - Annals of Mathematical Logic 7 (2):267.

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Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.
The Countable Admissible Ordinal Equivalence Relation.William Chan - 2017 - Annals of Pure and Applied Logic 168 (6):1224-1246.
Computable Abelian Groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Strange Structures From Computable Model Theory.Howard Becker - 2017 - Notre Dame Journal of Formal Logic 58 (1):97-105.

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