  We study a well-known technique of using absoluteness for giving choice-free
proofs to some statements which are known to be provable with the axiom of
choice. The idea is to reduce the problem to an inner model where the axiom of
choice holds and use absoluteness. We examine the complexity of the sentences
that this technique can be applied to, and show that many of the theorems in
basic partition calculus have the adequate complexity for this technique to
apply.
