Browse/search for people

Publication - Professor Philip Welch

    Obtaining Woodin's cardinals

    Citation

    Welch, PD, 2017, ‘Obtaining Woodin's cardinals’. in: Andres Eduardo Caicedo, James Cummings, Peter Koellner, Paul B Larson (eds) Foundations of Mathematics: Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday, March 27-29 2015, Harvard University, Cambridge, MA. American Mathematical Society, pp. 161-176

    Abstract

    Since the 1980’s work on Projective Determinacy and ADL(R) the concept of Woodin cardinal has become to be seen as central in the theory of large cardinals and inner model theory. The use by Woodin himself of a background assumption in many arguments that the universe contains unboundedly many such cardinals again draws attention to the centrality of this concept.

    As is well known the Reflection Principles dating to a more classicial era only provide large cardinals consistent with V = L, and not the wherewithal for such theorems on absoluteness under set forcing that Woodin has proven.

    We discuss here a reflection principle derived from weak sub-compactness that implies the existence of a proper class of measurable Woodin cardinals - thus providing adequate background assumptions for many of Woodin’s absoluteness results in his work

    Full details in the University publications repository