Axiomatizing Kolmogorov Complexity
We revisit the axiomatization of Kolmogorov complexity given by Alexander Shen, currently available only in Russian language. We derive an axiomatization for conditional plain Kolmogorov complexity. Next we show that the axiomatic system given by Shen cannot be weakened (at least in any natural way). In addition we prove that the analogue of Shen’s axiomatic system fails to characterize prefix-free Kolmogorov complexity.