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Bounded Immunity and BttReductions
 MLQ Math. Log. Q
, 1999
"... We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that # # does not ktt reduce to a kimmune set, which improves a previous result by Kobzev [7, 13]. We apply the result to show that ..."
Abstract

Cited by 6 (2 self)
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We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that # # does not ktt reduce to a kimmune set, which improves a previous result by Kobzev [7, 13]. We apply the result to show that # # does not bttreduce 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 e#ectively simple sets and show that simple sets are not bttcuppable. Keywords: Computability, Recursion Theory, bounded reducibilities, minimal programs, immunity, kimmune, regressive, retraceable, e#ectively simple, cuppable. 1 Introduction There seems to be a large gap between immunity and hyperimmunity (himmunity) that is waiting to be filled. What happens, one wonders if the disjoint strong arrays that try to witness that a set is not himmune are subjected to additional conditions...
A Note on a Variant of Immunity, BttReducibility, and Minimal Programs
, 1996
"... We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that K does not ktt reduce to a kimmune set which improves a previous result by Kobzev [6]. We apply the result to show that K does ..."
Abstract
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We define and study a new notion called kimmunity that lies between immunity and hyperimmunity in strength. Our interest in kimmunity is justified by the result that K does not ktt reduce to a kimmune set which improves a previous result by Kobzev [6]. We apply the result to show that K does not bttreduce 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