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, ...

I’m teaching Edinburgh’s undergraduate Axiomatic Set Theory course, and the axioms we’re using are Lawvere’s Elementary Theory of the Category of Sets — with the twist that everything’s going to be ...

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 ...

ACL2 is a first-order, essentially quantifier free logic of computable recursive functions based on an applicative subset of Common Lisp. It supports lists as a primitive data structure. We describe ...

Abstract: This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random ...

Abstract: The characters and disadvantages of some main present score functions in the vague set theory are analyzed. The meaning and essence of score functions are discussed and the concept of vague ...

In this elementary paper we establish a few novel results in set theory; their interest is wholly foundational-philosophical in motivation. We show that in Cantor-Von Neumann Set-Theory (CVN), which ...