BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Beyond the infinite: Rothschild Distinguished Visiting Professor L
 ecture - Woodin\, H (Harvard University)
DTSTART:20151005T150000Z
DTEND:20151005T160000Z
UID:TALK61289@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:The modern mathematical story of infinity began in the period 
 1879-84 with a series of papers by Cantor that defined the fundamental fra
 mework of the subject. Within 40 years the key ZFC axioms for Set Theory w
 ere in place and the stage was set for the detailed development of transfi
 nite mathematics\, or so it seemed.  However\, in a completely unexpected 
 development\, Cohen showed in 1963 that even the most basic problem of Set
  Theory\, that of Cantor's Continuum Hypothesis\, was not solvable on the 
 basis of the ZFC axioms.\n\nThe 50 years since Cohen's work has seen a vas
 t development of Cohen's method and the realization that the occurrence of
  unsolvable problems is ubiquitous in Set Theory. This arguably challenges
  the very conception of Cantor on which Set Theory is based.\n\nThus a fun
 damental dilemma has emerged. On the one hand\, the discovery\, also over 
 the last 50 years\, of a rich hierarchy axioms of infinity seems to argue 
 that Cantor's conception is fundamentally sound. But on the other hand\, t
 he developments of Cohen's method over this same period seem to strongly s
 uggest there can be no preferred extension of the ZFC axioms to a system o
 f axioms that can escape the ramifications of Cohen's method.\n\nBut this 
 dilemma was itself based on a misconception and recent discoveries suggest
  there is a resolution.\n
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR