Journal of Symbolic Logic

Computable categoricity of trees of finite height

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.

Article information

Source
J. Symbolic Logic Volume 70, Issue 1 (2005), 151-215.

Dates
First available in Project Euclid: 1 February 2005

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1107298515

Digital Object Identifier
doi:10.2178/jsl/1107298515

Mathematical Reviews number (MathSciNet)
MR2119128

Zentralblatt MATH identifier
05004793

Citation

Lempp, Steffen; McCoy, Charles; Miller, Russell; Solomon, Reed. Computable categoricity of trees of finite height. J. Symbolic Logic 70 (2005), no. 1, 151--215. doi:10.2178/jsl/1107298515. http://projecteuclid.org/euclid.jsl/1107298515.

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