Set theory, the mathematical study of collections of objects, forms a foundation for much of modern mathematics, while cardinal functions provide a means to quantify the sizes of these sets, ...

A Platonistic set theory with a universal set, CUSɩ, in the spirit of Alonzo Church's "Set Theory with a Universal Set," is presented; this theory uses a different sequence of restricted equivalence ...

Mathematics often helps us to think about issues that don’t seem mathematical. One area that has surprisingly far-reaching applications is the theory of sets. Sets are one of the most basic objects in ...

A key fact in the theory of Boolean functions f: {0, 1}n → {0, 1} is that they often undergo sharp thresholds. For example, if the function f: {0, 1}n → {0, 1} is monotone and symmetric under a ...