# Every Δ20 Degree is a Strong Degree of Categoricity

Journal of mathematical logic（2022）

Abstract

A strong degree of categoricity is a Turing degree [Formula: see text] such that there is a computable structure [Formula: see text] that is [Formula: see text]-computably categorical (there is a [Formula: see text]-computable isomorphism between any two computable copies of [Formula: see text]), and such that there exist two computable copies of [Formula: see text] between which every isomorphism computes [Formula: see text]. The question of whether every [Formula: see text] degree is a strong degree of categoricity has been of interest since the first paper on this subject. We answer the question in the affirmative, by constructing an example.

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Key words

Computable structure theory,degrees of categoricity,isomorphisms,Turing degrees

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