Every Δ20 degree is a strong degree of categoricity

Journal of Mathematical Logic 22 (3) (2022)
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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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Degrees That Are Not Degrees of Categoricity.Bernard Anderson & Barbara Csima - 2016 - Notre Dame Journal of Formal Logic 57 (3):389-398.

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