My question is on the relation of this two principles.
For instance, in the of Intuitionistic set theory we can prove Zorns Lemma (but Zorns Lemma will not be equivalent to the axiom of choice, since choice implies tertium non datur). Suppose now you have a paraconsistent set theory which models Zorns Lemma. It is reasonable to assume that in this case Zorns Lemma and axiom of choice are equivalent ?
Does the axiom of choice imply the principle of explosion ?
Could you recomend me some literature on this ?