Set theory is about more than describing sets. Just as, in arithmetic, you learn to apply arithmetical operations to numbers—for example, addition or multiplication—you can also define set ...

We define an open symmetric two-place relation on the reals such that the reals cannot be covered by countably many sets of related elements, but there is no uncountable set of unrelated elements. The ...

Peter Bruyns, Henry Rose, Varieties with Cofinal Sets: Examples and Amalgamation, Proceedings of the American Mathematical Society, Vol. 111, No. 3 (Mar., 1991), pp ...