Index sets in computable analysis

Π 0 1 classes in a space X where X equals {0, 1} ω, ω ω, [0, 1], or the real line real are given an effective enumeration P e, X and the computably continuous functions are given an effective enumeration F e, X. The notion of index sets associated with Π 0 1 classes and with computably continuous functions is developed. The complexity of various problems of analysis is determined by the complexity of the associated index set.

Authors

• Douglas Cenzer
• Jeffrey B. Remmel

Keywords

• Index set
• Pi-0-1 class
• Computable analysis