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:
“The only effective way to help well-intentioned, intelligent persons to do the best they can in raising children is to encourage and guide them always to do their own thinking in their attempts at understanding and dealing with child-rearing situations and problems, and not to rely blindly on the opinions of others.”
—Bruno Bettelheim (20th century)
“I hate the whole race.... There is no believing a word they say—your professional poets, I mean—there never existed a more worthless set than Byron and his friends for example.”
—Arthur Wellesley, 1st Duke Wellington (1769–1852)
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)