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March 2006 Computable trees of Scott rank ω 1CK, and computable approximation
Wesley Calvert, Julia F. Knight, Jessica Millar
J. Symbolic Logic 71(1): 283-298 (March 2006). DOI: 10.2178/jsl/1140641175

Abstract

Makkai [10] produced an arithmetical structure of Scott rank ω1CK. In [9], Makkai’s example is made computable. Here we show that there are computable trees of Scott rank ω1CK. 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 ω1CK that is “strongly computably approximable”. We also develop some technology that may yield further results of this kind.

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Wesley Calvert. Julia F. Knight. Jessica Millar. "Computable trees of Scott rank ω 1CK, and computable approximation." J. Symbolic Logic 71 (1) 283 - 298, March 2006. https://doi.org/10.2178/jsl/1140641175

Information

Published: March 2006
First available in Project Euclid: 22 February 2006

zbMATH: 1112.03039
MathSciNet: MR2210068
Digital Object Identifier: 10.2178/jsl/1140641175

Rights: Copyright © 2006 Association for Symbolic Logic

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Vol.71 • No. 1 • March 2006
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