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Archive for Mathematical Logic

, Volume 42, Issue 3, pp 279–291 | Cite as

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.).

Keywords

Computable Structure Effectiveness Condition Countable Structure Immune Relation Computable Copy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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