Has there been any mathematical research on redundancy in axiom sets?

Question

This is a bit of a soft question, but has there been any significant research on redundancy in axiom sets? Let me explain what I mean. I know that a few papers deal with proving that a particular axiom is or is not redundant from a set of axioms. However, I am talking about something a little different, and more advanced. It could happen that once a particular axiom is deleted, some other axiom, which was also redundant from the original set, is now non-redundant. Let me give a concrete example. Take the set of axioms that characterize strict partial orders. The three axioms are Anti-reflexivity, Asymmetry, and Transitivity. In this set, Anti-reflexivity and Asymmetry are, individually, redundant, but if either one is deleted the other axiom becomes non-redundant. It could also happen that once a redundant axiom is deleted, some other axiom which was also redundant from the original set is still redundant from the original set. So, has there been any research into this type of question? I would like some references for this.