Abstract:
In this survey, we discuss computability spectra of countable structures that provide a natural measure of noncomputability of a structure. This notion is a main tool of investigating algorithmic properties of countable structures. Along with a review of known results in this field, we present proofs of some new results to illustrate the method of interpretation which is a basic method of the field. We also discuss some remaining open questions.
Keywords:structure, computable structure, spectrum of a structure, interpretation.