Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.The same first-order language with "" and "" of classical set theory is usually used, so this is not to be confused with a constructive types approach.On the other hand, some constructive theories are indeed motivated by their interpretability in type theories. In addition to rejecting the law of excluded middle , constructive set theories often require some logical quantifiers in their axioms to be bounded, motivated by results tied to impredicativity.