Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. That is, it uses the usual first-order language of classical set theory, and although of course the logic is constructive, there is no explicit use of constructive types. Rather, there are just sets, thus it can look very much like classical mathematics done on the most common foundations, namely the Zermelo–Fraenkel axioms (ZFC).
Read more about Constructive Set Theory: Intuitionistic Zermelo–Fraenkel, Myhill's Constructive Set Theory, Aczel's Constructive Zermelo–Fraenkel, Interpretability in Type Theory, Interpretability in Category Theory
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