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 desert is a natural extension of the inner silence of the body. If humanity’s language, technology, and buildings are an extension of its constructive faculties, the desert alone is an extension of its capacity for absence, the ideal schema of humanity’s disappearance.”
—Jean Baudrillard (b. 1929)
“I set forth a humble and inglorious life; that does not matter. You can tie up all moral philosophy with a common and private life just as well as with a life of richer stuff. Each man bears the entire form of man’s estate.”
—Michel de Montaigne (1533–1592)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)