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:
“... the constructive power of an image is not measured in terms of its truth, but of the love it inspires.”
—Sarah Patton Boyle, U.S. civil rights activist and author. The Desegregated Heart, part 1, ch. 15 (1962)
“I never can hear a crowd of people singing and gesticulating, all together, at an Italian opera, without fancying myself at Athens, listening to that particular tragedy, by Sophocles, in which he introduces a full chorus of turkeys, who set about bewailing the death of Meleager.”
—Edgar Allan Poe (1809–1845)
“Won’t this whole instinct matter bear revision?
Won’t almost any theory bear revision?
To err is human, not to, animal.”
—Robert Frost (1874–1963)