Application of set theory subjects as ordinals, forcing, generic filters in software engineering I am going to teach a course in set theory for software engineering students.
I am going to talk in this course about: ordinal numbers, partial orders, well ordering, generic filters and maybe some cardinal invariants (such as $\mathfrak b$, $\mathfrak d$). I might also give a gentel introduction to forcing theory. 

I was asked by the head of the department, to add to this course some application of this theory to software engineering.

Since my main area is math and not computer science, I don't have an idea for such an application.

Any ideas for such an application? If there is I would be greatfull if you could give me a detailed source.

Thank you!
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.