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Relatively Hyperimmune Relations on Structures

Authors:	S S Goncharov C F McCoy J F Knight V S Harizanov

Institution:	(1) Institute of Mathematics SB RAS, Akademika Koptyuga Prospekt, 4, Novosibirsk, 630090, Russia;(2) Department of Mathematics, University of Wisconsin, Madison, Madison, WI 53706, USA;(3) Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA;(4) Department of Mathematics, The George Washington University, Washington, D.C 20052, USA

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 $\neg R$ is h-simple (h-immune) relative to ${\mathcal{B}}$ .

Keywords:	computable structure relatively hyperimmune relation relatively hypersimple relation
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