Geodesic
Relatively Hyperimmune Relations on Structures
Algebra i logika, Tome 43 (2004) no. 2, pp. 170-183

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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 $\mathcal{B}$.
Keywords: computable structure, relatively hyperimmune relation, relatively hypersimple relation. 
@article{AL_2004_43_2_a2,
     author = {S. S. Goncharov and Ch. F. McCoy and J. F. Knight and V. S. Harizanova},
     title = {Relatively {Hyperimmune} {Relations} on {Structures}},
     journal = {Algebra i logika},
     pages = {170--183},
     publisher = {mathdoc},
     volume = {43},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_2_a2/}
}
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S. S. Goncharov; Ch. F. McCoy; J. F. Knight; V. S. Harizanova. Relatively Hyperimmune Relations on Structures. Algebra i logika, Tome 43 (2004) no. 2, pp. 170-183. http://geodesic.mathdoc.fr/item/AL_2004_43_2_a2/