 Mathematics can be based on set theory. This means that mathematical objects are construed as sets and their properties are derived from the axioms of set theory. The intuitive informal picture behind set theory is that there is a cumulative hierarchy \(V_\alpha\) (\(\alpha\) an ordinal) of sets and the axioms are intended to describe the basic properties of such sets. This kind of set theoretical foundation of mathematics has become widely accepted among working mathematicians. We refer to the SEP entry on  set theory  for more details. Alternatives to set theory are at least  category theory,  constructive mathematics, and second-order logic.