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The ω-Turing degrees

Authors
Journal
Annals of Pure and Applied Logic
0168-0072
Publisher
Elsevier
Volume
165
Issue
9
Identifiers
DOI: 10.1016/j.apal.2014.04.017
Keywords
  • Turing Reducibility
  • ω-Enumeration Degrees
  • Degrees Structures

Abstract

Abstract In this paper we initiate the study of the ω-Turing reducibility between sequences of sets of natural numbers. We shall prove that the induced degree structure is an extension of the structure of the Turing degrees and that the two structures are closely connected, but different enough. Further we shall prove some definability results for the local theory of the newly defined structure.

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