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1-Generic Enumeration Degrees Below O e ’

In: Mathematical Logic

Author

Listed:
  • C. S. Copestake

    (University of Leeds, Department of Pure Mathematics)

Abstract

Enumeration reducibility is the formalisation of the natural concept of relative enumerability between sets of natural numbers. A set A is said to be enumeration reducible to a set B iff there is some effective procedure which gives an enumeration of A from any enumeration of B. This can be shown to be equivalent to the following definition: Definition 1.1 A set of natural numbers A is enumeration reducible (e-reducible,≦e) to a set of natural numbers B iff there is an i such that for all x $$x \in A \Leftrightarrow \exists z\left[ {\langle x,z\rangle \in {W_i}\& {D_z} \subset B} \right]$$ where W i and D z are, respectively, the i th recursively enumerable set and the z th finite set in appropriate standard listing of such sets.

Suggested Citation

  • C. S. Copestake, 1990. "1-Generic Enumeration Degrees Below O e ’," Springer Books, in: Petio Petrov Petkov (ed.), Mathematical Logic, pages 257-265, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0609-2_17
    DOI: 10.1007/978-1-4613-0609-2_17
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