Descriptive Set Theory - Effective Descriptive Set Theory

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:

    Relying on any one disciplinary approach—time-out, negotiation, tough love, the star system—puts the parenting team at risk. Why? Because children adapt to any method very quickly; today’s effective technique becomes tomorrow’s worn dance.
    Ron Taffel (20th century)

    The extra worry began it—on the
    Blue blue mountain—she never set foot
    And then and there. Meanwhile the host
    Mourned her quiet tenure. They all stayed chatting.
    No one did much about eating.
    John Ashbery (b. 1927)

    By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.
    Abraham Lincoln (1809–1865)