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March 2005 Computable categoricity of trees of finite height
Steffen Lempp, Charles McCoy, Russell Miller, Reed Solomon
J. Symbolic Logic 70(1): 151-215 (March 2005). DOI: 10.2178/jsl/1107298515

Abstract

We characterize the structure of computably categorical trees of finite height, and prove that our criterion is both necessary and sufficient. Intuitively, the characterization is easiest to express in terms of isomorphisms of (possibly infinite) trees, but in fact it is equivalent to a Σ03-condition. We show that all trees which are not computably categorical have computable dimension ω. Finally, we prove that for every n≥ 1 in ω, there exists a computable tree of finite height which is δ0n+1-categorical but not δ0n-categorical.

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Steffen Lempp. Charles McCoy. Russell Miller. Reed Solomon. "Computable categoricity of trees of finite height." J. Symbolic Logic 70 (1) 151 - 215, March 2005. https://doi.org/10.2178/jsl/1107298515

Information

Published: March 2005
First available in Project Euclid: 1 February 2005

zbMATH: 1104.03026
MathSciNet: MR2119128
Digital Object Identifier: 10.2178/jsl/1107298515

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 1 • March 2005
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