Effective Descriptive Set Theory
The area of effective descriptive set theory combines the methods of descriptive set theory with those of generalized recursion theory (especially hyperarithmetical theory). In particular, it focuses on lightface analogues of hierarchies of classical descriptive set theory. Thus the hyperarithmetic hierarchy is studied instead of the Borel hierarchy, and the analytical hierarchy instead of the projective hierarchy. This research is related to weaker version of set theory such as Kripke-Platek set theory and second-order arithmetic.
Read more about this topic: Descriptive Set Theory
Famous quotes containing the words effective, set and/or theory:
“I know no method to secure the repeal of bad or obnoxious laws so effective as their stringent execution.”
—Ulysses S. Grant (1822–1885)
“I set it down as a fact that if all men knew what each said of the other, there would not be four friends in the world.”
—Blaise Pascal (1623–1662)
“The great tragedy of science—the slaying of a beautiful theory by an ugly fact.”
—Thomas Henry Huxley (1825–1895)