Simple and immune relations on countable structures

Sergei. S. Goncharov, Valentina. S. Harizanov, Julia. F. Knight, Charles F. D. McCoy
<span title="2003-04-01">2003</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3egevcnserbbni4tcigsztdici" style="color: black;">Archive for Mathematical Logic</a> </i> &nbsp;
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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