This article is cited in 2 papers

Relatively Hyperimmune Relations on Structures

S. S. Goncharov^a, Ch. F. McCoy^b, J. F. Knight^c, V. S. Harizanova<sup>d

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b University of Wisconsin-Madison
^c University of Notre Dame
^d George Washington University

Abstract: 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.

UDC: 510.53

Received: 23.04.2002

 English version: Algebra and Logic, 2004, 43:2, 94–101

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