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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Beyond the infinite: Rothschild Distinguished Visi
ting Professor Lecture - Woodin\, H (Harvard Unive
rsity)
DTSTART;TZID=Europe/London:20151005T160000
DTEND;TZID=Europe/London:20151005T170000
UID:TALK61289AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61289
DESCRIPTION:The modern mathematical story of infinity began in
the period 1879-84 with a series of papers by Can
tor that defined the fundamental framework of the
subject. Within 40 years the key ZFC axioms for Se
t Theory were in place and the stage was set for t
he detailed development of transfinite mathematics
\, or so it seemed. However\, in a completely une
xpected development\, Cohen showed in 1963 that ev
en the most basic problem of Set Theory\, that of
Cantor's Continuum Hypothesis\, was not solvable o
n the basis of the ZFC axioms.\n\nThe 50 years sin
ce Cohen's work has seen a vast development of Coh
en's method and the realization that the occurrenc
e of unsolvable problems is ubiquitous in Set Theo
ry. This arguably challenges the very conception o
f Cantor on which Set Theory is based.\n\nThus a f
undamental 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. B
ut on the other hand\, the developments of Cohen's
method over this same period seem to strongly sug
gest there can be no preferred extension of the ZF
C axioms to a system of axioms that can escape the
ramifications of Cohen's method.\n\nBut this dile
mma was itself based on a misconception and recent
discoveries suggest there is a resolution.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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