A Computably Categorical Structure Whose Expansion by a
Constant Has Infinite Computable Dimension
Status: published in the Journal of
Symbolic Logic, vol. 68 (2003), pp. 1199 - 1241.
Availability: DVI, PostScript, PDF
Abstract. 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 omega. Our proof uses a version
of Goncharov's method of left and right operations.