Abstract

We define and study a new notion called k-immunity that lies between immunity and hyperimmunity in strength. Our interest in k-immunity is justified by the result that K does not k-tt reduce to a k-immune set which improves a previous result by Kobzev [6]. We apply the result to show that K does not btt-reduce to MIN, the set of minimal programs. Other applications include the set of Kolmogorov random strings, and retraceable and regressive sets. We also give a new characterization of effectively simple sets, and add some results about regressive sets. Keywords: Computability, bounded reducibilities, minimal programs, immunity. 1

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