Recursive Properties of Intervals of Recursive Linear Orders

  • Geoffrey Hird
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 12)


We investigate the possible recursive properties of intervals, and other suborderings, of recursive linear orders. Let A be a recursive linear order with a co-r.e. interval P. We characterize those (A, P) for which there exists a recursive linear order ℬ and an isomorphism f: ℬ ≅ A such that f -1 (P) is (a) not r.e.; (b) immune; (c) hyperimmune. We give general sufficient conditions for A and the subset P under which there exist such ℬ and f with f -1(P) exhibiting the above properties. We show, that no interval P can be hyperhyperimmune (or even strongly hyperimmune).


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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Geoffrey Hird
    • 1
  1. 1.ORA Corp.IthacaUSA

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