A computably categorical structure whose expansion by a constant has infinite computable dimension

Cholak, Goncharov, Khoussainov, and Shore [J. Symbolic Logic 64 (1999) 13– 37] 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. ∗Partially supported by an Alfred P. Sloan Doctoral Dissertation Fellowship and NSF Grant DMS0200465. ∗∗Partially supported by NSF Grants DMS-0100035 and INT-9602579. Thanks also to the Mathematics Departments at Harvard and MIT for their hospitality.