Cool Logic

Robert PaƟmann (ILLC)

One Axiom to Rule Them All

November 4th at 17:30, in F1.15

One does not simply control cardinals below the continuum... Or do we? We will present in a non-technical way some examples for strange and surprising behaviour of infinite cardinals below the continuum. This becomes a lot more fun when the continuum hypothesis fails, especially with our one axiom to rule them all: Martin's Axiom. We will introduce Martin's Axiom and use it to control the behaviour of cardinals below the continuum. If time permits, we will sketch how to construct a model of Martin's Axiom in which the continuum hypothesis fails.