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 R (¬R, 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 R (¬R, resp.) is simple (immune, resp.).
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Received: 4 February 2001 Published online: 5 November 2002
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ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.
RID="*"
ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.
RID="*"
ID="*" The first three authors gratefully acknowledge support of the NFS Binational Grant DMS-0075899.
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Goncharov, S., Harizanov, V., Knight, J. et al. Simple and immune relations on countable structures. Arch. Math. Logic 42, 279–291 (2003). https://doi.org/10.1007/s00153-002-0150-2
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DOI: https://doi.org/10.1007/s00153-002-0150-2