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
Famous quotes containing the words constructive, set and/or theory:
“If grandparents want to have a meaningful and constructive role, the first lesson they must learn is that becoming a grandparent is not having a second chance at parenthood!”
—Eda Le Shan (20th century)
“You have a row of dominoes set up; you knock over the first one, and what will happen to the last one is that it will go over very quickly.”
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“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes “So much the worse for the facts: let them be altered,” instead of “So much the worse for my theory.””
—George Bernard Shaw (1856–1950)