1-Generic Enumeration Degrees Below O e ’

C. S. Copestake
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C. S. Copestake: University of Leeds, Department of Pure Mathematics

A chapter in Mathematical Logic, 1990, pp 257-265 from Springer

Abstract: 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.

Date: 1990
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DOI: 10.1007/978-1-4613-0609-2_17

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