We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both computable categoricity and relative computable categoricity and its relativizations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm221-2-2,
author = {Rodney G. Downey and Asher M. Kach and Steffen Lempp and Daniel D. Turetsky},
title = {Computable categoricity versus relative computable categoricity},
journal = {Fundamenta Mathematicae},
volume = {220},
year = {2013},
pages = {129-159},
zbl = {1320.03070},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm221-2-2}
}
Rodney G. Downey; Asher M. Kach; Steffen Lempp; Daniel D. Turetsky. Computable categoricity versus relative computable categoricity. Fundamenta Mathematicae, Tome 220 (2013) pp. 129-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm221-2-2/