Determinator - Determinacy and Large Cardinals

Determinacy and Large Cardinals

There is an intimate relationship between determinacy and large cardinals. In general, stronger large cardinal axioms prove the determinacy of larger pointclasses, higher in the Wadge hierarchy, and the determinacy of such pointclasses, in turn, proves the existence of inner models of slightly weaker large cardinal axioms than those used to prove the determinacy of the pointclass in the first place.

Read more about this topic:  Determinator

Other articles related to "determinacy and large cardinals, determinacy, cardinals":

Determinator - Determinacy and Large Cardinals - Axiom of Determinacy
... The axiom of determinacy, or AD, asserts that every two-player game of perfect information of length ω, in which the players play naturals, is determined ... However, if there are infinitely many Woodin cardinals with a measurable above them all, then L(R) is a model of ZF that satisfies AD ...

Famous quotes containing the word large:

    The elements of success in this business do not differ from the elements of success in any other. Competition is keen and bitter. Advertising is as large an element as in any other business, and since the usual avenues of successful exploitation are closed to the profession, the adage that the best advertisement is a pleased customer is doubly true for this business.
    Madeleine [Blair], U.S. prostitute and “madam.” Madeleine, ch. 5 (1919)