Application of set theory subjects as ordinals, forcing, generic filters in software engineering
Generally speaking, if you want to present some applications of the theory, it's more effective to start with applications first and teach the theory that's needed for that application, rather than select a collection of theory and then search around for some application of it.

So, one way to approach your question is to ask why the department wants software engineers to know set theory. How will set theory help software engineers?  Then once you know the answer to that question, you could devise a curriculum based upon the elements of set theory that will be relevant to software engineers.  Most likely the set of topics that should be taught to software engineers is quite different from the set of topics that we would teach to mathematicians.

If you've followed this approach to course design, you should able to answer very clearly what the applications are and why you are teaching them this material.  This approach can also potentially lead to better student engagement, depending on student's motivations.  However, this approach likely requires re-thinking the entire course and starting over from scratch on the syllabus and topics you plan to teach, which might or might not be attractive in this case.