A computably categorical structure whose expansion by a constant has infinite computable dimension
Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore · Journal of Symbolic Logic · 2003
Abstract Cholak, Goncharov, Khoussainov, and Shore [1] showed that for each k > 0 there is a computably categorical structure whose expansion by a constant has computable dimension k. We show that the same is true with k replaced by ω. Our proof uses a version of Goncharov's method of left and right operations.