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Infima of d.r.e. degrees

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Abstract

Lachlan observed that the infimum of two r.e. degrees considered in the r.e. degrees coincides with the one considered in the \({\Delta_2^0}\) degrees. It is not true anymore for the d.r.e. degrees. Kaddah proved in (Ann Pure Appl Log 62(3):207–263, 1993) that there are d.r.e. degrees a, b, c and a 3-r.e. degree x such that a is the infimum of b, c in the d.r.e. degrees, but not in the 3-r.e. degrees, as a < x < b, c. In this paper, we extend Kaddah’s result by showing that such a structural difference occurs densely in the r.e. degrees. Our result immediately implies that the isolated 3-r.e. degrees are dense in the r.e. degrees, which was first proved by LaForte.

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Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Jiang Liu, Shenling Wang & Guohua Wu

Authors
  1. Jiang Liu
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  2. Shenling Wang
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  3. Guohua Wu
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Corresponding author

Correspondence to Shenling Wang.

Additional information

An extended abstract of this paper was published in [7], CiE 2009, Heidelberg. Wu is partially supported by NTU grant RG58/06, M52110023.

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Liu, J., Wang, S. & Wu, G. Infima of d.r.e. degrees. Arch. Math. Logic 49, 35–49 (2010). https://doi.org/10.1007/s00153-009-0159-x

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  • DOI: https://doi.org/10.1007/s00153-009-0159-x

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