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Relatively hyperimmune relations on structures. (Russian, English) Zbl 1115.03048
Algebra Logika 43, No. 2, 170-183 (2004); translation in Algebra Logic 43, No. 2, 94-101 (2004).
Summary: Let $$\mathcal A$$ be a computable structure and let $$R$$ be an additional relation on its domain. We establish a necessary and sufficient condition for the existence of an isomorphic copy $$\mathcal B$$ of $$\mathcal A$$ such that the image of $$R$$ ($$\lnot R$$) is $$h$$-simple ($$h$$-immune) relative to $$\mathcal B$$.
MSC:
 03D45 Theory of numerations, effectively presented structures 08A02 Relational systems, laws of composition
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