Degree spectra and computable dimensions in algebraic structures

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 Partially supported by an Alfred P. Sloan Doctoral Dissertation Fellowship. Current address: Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago IL 60637, U.S.A.. Partially supported by NSF Grants DMS-9503503, DMS-9802843, and INT-9602579. 1 

• Type: Journal
• Year: 2002
• Where: APAL
• Authors: Denis R. Hirschfeldt, Bakhadyr Khoussainov, Richard A. Shore, Arkadii M. Slinko
• Keywords: APAL 2002, Interesting Computability-theoretic Property, Similar Examples, Well-known Classes