Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities

Details Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities

2008-01-02

arxiv.org/abs/0801.0350v1

Mathematics

Logic

41 pages

Scientific paper

We introduce orderings between total functions f,g: N -> N which refine the pointwise "up to a constant" ordering <=cte and also insure that f(x) is often much less thang(x). With such orderings, we prove a strong hierarchy theorem for Kolmogorov complexities obtained with jump oracles and/or Max or Min of partial recursive functions. We introduce a notion of second order conditional Kolmogorov complexity which yields a uniform bound for the "up to a constant" comparisons involved in the hierarchy theorem.

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