Computable categoricity and the Ershov hierarchy

Annals of Pure and Applied Logic 156 (1):86-95 (2008)
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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

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References found in this work

Limiting recursion.E. Mark Gold - 1965 - Journal of Symbolic Logic 30 (1):28-48.
Δ20-categoricity in Boolean algebras and linear orderings.Charles F. D. McCoy - 2003 - Annals of Pure and Applied Logic 119 (1-3):85-120.
A proof of Beigel's cardinality conjecture.Martin Kummer - 1992 - Journal of Symbolic Logic 57 (2):677-681.

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