![]() | This article may be too technical for most readers to understand.(February 2023) |
In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number such that for all functions , there exists a cardinal with and an elementary embedding from the Von Neumann universe into a transitive inner model with critical point and .
An equivalent definition is this: is Woodin if and only if is strongly inaccessible and for all there exists a which is --strong.
being --strong means that for all ordinals , there exist a which is an elementary embedding with critical point , , and . (See also strong cardinal.)
A Woodin cardinal is preceded by a stationary set of measurable cardinals, and thus it is a Mahlo cardinal. However, the first Woodin cardinal is not even weakly compact.
© MMXXIII Rich X Search. We shall prevail. All rights reserved. Rich X Search