[ogogmad]

You mean countability as a term in set theory. How is axiomatic set theory useful in computer science?

Axiomatic set theory is a non-constructive theory. Many results in set theory depend on the existence of functions which cannot be computed. Or assert that something exists without providing any means of finding it. Even the Cantor-Schroeder-Bernstein theorem asserts the existence of something that cannot be explicitly constructed.

I fail to see how any of it has any connection to computing.

More broadly, I think many computing people are too uncritical about the relevance of mathematics like AST to their discipline. They are very likely to find themselves disappointed.