 Richardson's theorem

Richardson's theorem is a result in the field of mathematical logic, specifically in the area of computability theory. The theorem states that if \( A \) is a recursively enumerable (r.e.) set, then the set of its recursive subsets is r.e. This theorem has significant implications for understanding the structure of recursively enumerable sets and their relationships to recursive sets. In more technical terms, the theorem provides a comprehensive characterization of the recursive subsets of a recursively enumerable set in terms of effective enumerability.