Reflexive Structures

Luis E. Sanchis
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Luis E. Sanchis: Syracuse University, School of Computer and Information Science

Chapter Chapter 4 in Reflexive Structures, 1988, pp 100-162 from Springer

Abstract: 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).

Date: 1988
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DOI: 10.1007/978-1-4612-3878-2_4

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