  We consider classical representations of integers: Church's function
iterators, cardinal equivalence classes of sets, ordinal equivalence classes of
totally ordered sets. Since programs do not work on abstract entities and
require formal representations of objects, we effectivize these abstract
notions in order to allow them to be computed by programs. To any such
effectivized representation is then associated a notion of Kolmogorov
complexity. We prove that these Kolmogorov complexities form a strict hierarchy
which coincides with that obtained by relativization to jump oracles and/or
allowance of infinite computations.
