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Degree spectra and computable dimension in algebraic structures

By Denis R. Hirschfeldt and Richard A. Shore


Abstract Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the given class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a \Lambda Partially supported by an Alfred P. Sloan Doctoral Dissertation Fellowship. Current address

Year: 2002
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