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Reflexive Structures

In: Reflexive Structures

Author

Listed:
  • Luis E. Sanchis

    (Syracuse University, School of Computer and Information Science)

Abstract

In this chapter we continue the study of classes closed under recursive operations, with emphasis on those classes of the form ℓ = RC(c), where c is some arbitrary function. There are many problems about these classes which cannot be solved with the techniques used in Chapter 2. For example, we do not know yet if ℓd = ℓde or ℓd ≠ ℓde. We shall see that both relations are possible, depending on the function c, but when c is a total function then ℓd ≠ ℓde, which means that there are predicates that are ℓd-enumerable (i.e., recursively enumerable in c) but are not recursive in c. Results of this type require a diagonalization technique, involving a kind of internal enumeration, or indexing for the class RC(c).

Suggested Citation

  • Luis E. Sanchis, 1988. "Reflexive Structures," Springer Books, in: Reflexive Structures, chapter 0, pages 100-162, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3878-2_4
    DOI: 10.1007/978-1-4612-3878-2_4
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