# DEGREES OF CATEGORICITY ON A CONE VIA η-SYSTEMS

@article{Csima2017DEGREESOC, title={DEGREES OF CATEGORICITY ON A CONE VIA $\eta$-SYSTEMS}, author={Barbara F. Csima and Matthew Harrison-Trainor}, journal={The Journal of Symbolic Logic}, year={2017}, volume={82}, pages={325 - 346} }

Abstract We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is ${\rm{\Delta }}_\alpha ^0 $ -complete for some α. To prove this, we extend Montalbán’s η-system framework to deal with limit ordinals in a more general way. We also show that, for any fixed computable structure, there is an ordinal α and a cone in the Turing degrees such…

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