Author:
Lempp Steffen,McCoy Charles,Miller Russell,Solomon Reed
Abstract
AbstractWe 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 -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 Σ30-categorical but not Δn3-categorical
Publisher
Cambridge University Press (CUP)
Reference35 articles.
1. Recursively presented Boolean algebras;LaRoche;Notices of the American Mathematical Society,1977
2. Enumerations, countable structures and Turing degrees
3. Kudinov O. V. , An integral domain with finite algorithmic dimension, unpublished manuscript.
4. An autostable 1-decidable model without a computable Scott family of ∃-formulas
Cited by
39 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Primitively Recursive Categoricity for Unars and Equivalence Structures;Siberian Mathematical Journal;2021-11
2. Index;Computable Structure Theory;2021-07-31
3. Bibliography;Computable Structure Theory;2021-07-31
4. Σ-Small Classes;Computable Structure Theory;2021-07-31
5. The Jump of A Structure;Computable Structure Theory;2021-07-31