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:
“Once we begin to appreciate that the apparent destructiveness of the toddler in taking apart a flower or knocking down sand castles is in fact a constructive effort to understand unity, we are able to revise our view of the situation, moving from reprimand and prohibition to the intelligent channeling of his efforts and the fostering of discovery.”
—Polly Berrien Berends (20th century)
“They smote and fell, who set the bars
Against the progress of the stars,
And stayed the march of Motherland!”
—Will Henry Thompson (1848–1918)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)