Refinment of the "up to a constant" ordering using contructive   co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov   complexities
  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. 
Marie Ferbus-Zanda (LIAFA), Serge Grigorieff (LIAFA)