# The Axiom of Determinacy implies that N1 is a Measurable Cardinal

#### by Zachiri McKenzie

Institution: The University of Melbourne
Date: Wed 7th May 2008
Time: 4:15 PM
Location: Room 215, Richard Berry Bldg, The University of Melbourne

Abstract: Solovayâ€™s realisation that the Axiom of Determinacy implies that N1 is
a measurable cardinal was hugely influential. It sparked a flurry of activity
amongst the set theoretic community that focused on investigating the links
between determinacy and large cardinals. In addition to giving birth to what
now can almost be classified as a sub-discipline in its own right, this result is
also a fascinating example of an oddity that can arise in a universe in which
the Axiom of Choice fails. In this talk I will briefly introduce the concept
of a measurable cardinal before presenting a proof of Solovayâ€™s result due to
D. A. Martin.