computable dimension
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2019 ◽  
Vol 170 (1) ◽  
pp. 58-94 ◽  
Author(s):  
Barbara F. Csima ◽  
Jonathan Stephenson
Keyword(s):  


2017 ◽  
Vol 55 (6) ◽  
pp. 461-484
Author(s):  
N. T. Kogabaev


2016 ◽  
Vol 55 (3-4) ◽  
pp. 519-534
Author(s):  
Oscar Levin


2009 ◽  
Vol 74 (1) ◽  
pp. 336-348
Author(s):  
Pavel Semukhin

AbstractWe study the following open question in computable model theory: does there exist a structure of computable dimension two which is the prime model of its first-order theory? We construct an example of such a structure by coding a certain family of c.e. sets with exactly two one-to-one computable enumerations into a directed graph. We also show that there are examples of such structures in the classes of undirected graphs, partial orders, lattices, and integral domains.



2005 ◽  
Vol 70 (1) ◽  
pp. 111-141 ◽  
Author(s):  
Russell Miller

AbstractWe prove that no computable tree of infinite height is computably categorical, and indeed that all such trees have computable dimension ω. Moreover, this dimension is effectively ω, in the sense that given any effective listing of computable presentations of the same tree, we can effectively find another computable presentation of it which is not computably isomorphic to any of the presentations on the list.



2005 ◽  
Vol 70 (1) ◽  
pp. 151-215 ◽  
Author(s):  
Steffen Lempp ◽  
Charles McCoy ◽  
Russell Miller ◽  
Reed Solomon

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



2004 ◽  
Vol 43 (6) ◽  
pp. 393-407 ◽  
Author(s):  
N. T. Kogabaev ◽  
O. V. Kudinov ◽  
R. Miller


2003 ◽  
Vol 68 (4) ◽  
pp. 1199-1241 ◽  
Author(s):  
Denis R. Hirschfeldt ◽  
Bakhadyr Khoussainov ◽  
Richard A. Shore

AbstractCholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.



2003 ◽  
Vol 175 (1) ◽  
pp. 102-143 ◽  
Author(s):  
Sergey S. Goncharov ◽  
Steffen Lempp ◽  
Reed Solomon


2002 ◽  
Vol 115 (1-3) ◽  
pp. 233-277 ◽  
Author(s):  
Denis R. Hirschfeldt


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