The computable dimension of trees of infinite height
Russell Miller · Journal of Symbolic Logic · 2005
Abstract We prove that no computable tree of infinite height is computably categorical, and indeed that all such trees have computable dimension ω. Moreover, this dimension is effectively ω, in the sense that given any effective listing of computable presentations of the same tree, we can effectively find another computable presentation of it which is not computably isomorphic to any of the presentations on the list.