Abstract
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).
This work formed part of the author’s doctoral dissertation at Monash University, Melbourne, Australia, under the supervision of Dr C.J. Ash. The author thanks Dr Ash for his guidance.
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© 1993 Springer Science+Business Media New York
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Hird, G. (1993). Recursive Properties of Intervals of Recursive Linear Orders. In: Crossley, J.N., Remmel, J.B., Shore, R.A., Sweedler, M.E. (eds) Logical Methods. Progress in Computer Science and Applied Logic, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0325-4_13
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DOI: https://doi.org/10.1007/978-1-4612-0325-4_13
Publisher Name: Birkhäuser, Boston, MA
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Online ISBN: 978-1-4612-0325-4
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