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|Title:||Computable categoricity and the Ershov hierarchy|
Graphs with finite components
|Source:||Khoussainov, B., Stephan, F., Yang, Y. (2008-11). Computable categoricity and the Ershov hierarchy. Annals of Pure and Applied Logic 156 (1) : 86-95. ScholarBank@NUS Repository. https://doi.org/10.1016/j.apal.2008.06.010|
|Abstract:||In this paper, the notions of Fα-categorical and Gα-categorical structures are introduced by choosing the isomorphism such that the function itself or its graph sits on the α-th level of the Ershov hierarchy, respectively. Separations obtained by natural graphs which are the disjoint unions of countably many finite graphs. Furthermore, for size-bounded graphs, an easy criterion is given to say when it is computable-categorical and when it is only G2-categorical; in the latter case it is not Fα-categorical for any recursive ordinal α. © 2008 Elsevier B.V. All rights reserved.|
|Source Title:||Annals of Pure and Applied Logic|
|Appears in Collections:||Staff Publications|
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