Archive for Mathematical Logic

, Volume 42, Issue 3, pp 279–291

Simple and immune relations on countable structures

  • Sergei. S. Goncharov
  • Valentina. S. Harizanov
  • Julia. F. Knight
  • Charles F. D. McCoy

Abstract.

 Let 𝒜 be a computable structure and let R be a new relation on its domain. We establish a necessary and sufficient condition for the existence of a copy ℬ of 𝒜 in which the image of RR, resp.) is simple (immune, resp.) relative to ℬ. We also establish, under certain effectiveness conditions on 𝒜 and R, a necessary and sufficient condition for the existence of a computable copy ℬ of 𝒜 in which the image of RR, resp.) is simple (immune, resp.).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sergei. S. Goncharov
    • 1
  • Valentina. S. Harizanov
    • 2
  • Julia. F. Knight
    • 3
  • Charles F. D. McCoy
    • 4
  1. 1.Academy of Sciences, Siberian Branch, Mathematical Institute, 630090 Novosibirsk, Russia. e-mail: gonchar@math.nsc.ruRU
  2. 2.Department of Mathematics, The George Washington University, Washington, D.C. 20052, USA. e-mail: harizanv@gwu.eduUS
  3. 3.Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA. e-mail: julia.f.knight.1@nd.eduUS
  4. 4.Department of Mathematics, University of Wisconsin, Madison, Madison, WI 53706, USA. e-mail: mccoy@math.wisc.eduUS

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