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The computable dimension of trees of infinite height. (English) Zbl 1098.03049
The author proves that every computable tree of infinite height has $$\omega$$ pairwisely non-computably isomorphic computable presentations. Moreover, given any computable enumeration of its computable presentations, one can effectively construct a computably isomorphic copy of this tree so that it will be not computably isomorphic to all presentations listed in this enumeration, i.e., the class of all computable presentations of such trees is effectively infinite.

##### MSC:
 03D45 Theory of numerations, effectively presented structures 03C57 Computable structure theory, computable model theory
##### Keywords:
computable dimension; computable model; autostability; tree
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##### References:
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