Relativizing computable categoricity

2021 ◽  
pp. 1
Author(s):  
Rodney G. Downey ◽  
Matthew Harrison-Trainor ◽  
Alexander Melnikov
Keyword(s):  
Computable Categoricity

scholarly journals The complexity of computable categoricity

2015 ◽  
Vol 268 ◽  
pp. 423-466 ◽  
Author(s):  
Rodney G. Downey ◽  
Asher M. Kach ◽  
Steffen Lempp ◽  
Andrew E.M. Lewis-Pye ◽  
Antonio Montalbán ◽  
...  
Keyword(s):  
Computable Categoricity

Equivalence structures and isomorphisms in the difference hierarchy

2009 ◽  
Vol 74 (2) ◽  
pp. 535-556 ◽  
Author(s):  
Douglas Cenzer ◽  
Geoffrey Laforte ◽  
Jeffrey Remmel
Keyword(s):  
Equivalence Relations ◽  
Computable Categoricity ◽  
Difference Hierarchy ◽  
The Difference

AbstractWe examine the effective categoricity of equivalence structures via Ershov's difference hierarchy. We explore various kinds of categoricity available by distinguishing three different notions of isomorphism available in this hierarchy. We prove several results relating our notions of categoricity to computable equivalence relations: for example, we show that, for such relations, computable categoricity is equivalent to our notion of weak ω-c.e. categoricity, and that -categoricity is equivalent to our notion of graph-ω-c.e. categoricity.

scholarly journals Computable categoricity and the Ershov hierarchy

2008 ◽  
Vol 156 (1) ◽  
pp. 86-95 ◽  
Author(s):  
Bakhadyr Khoussainov ◽  
Frank Stephan ◽  
Yue Yang
Keyword(s):  
Computable Categoricity ◽  
Ershov Hierarchy

scholarly journals Computable categoricity versus relative computable categoricity

2013 ◽  
Vol 221 (2) ◽  
pp. 129-159 ◽  
Author(s):  
Rodney G. Downey ◽  
Asher M. Kach ◽  
Steffen Lempp ◽  
Daniel D. Turetsky
Keyword(s):  
Computable Categoricity

scholarly journals Computable categoricity of trees of finite height

2005 ◽  
Vol 70 (1) ◽  
pp. 151-215 ◽  
Author(s):  
Steffen Lempp ◽  
Charles McCoy ◽  
Russell Miller ◽  
Reed Solomon
Keyword(s):  
Computable Categoricity ◽  
Finite Height ◽  
Computable Dimension ◽  
Infinite Trees ◽  
Necessary And Sufficient

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

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