Speaker: Jin Wei

Abstract: Continuum hypothesis is known to be independent from ZFC thanks to celebrated work of Gödel and Cohen. The story cannot end here as CH is unpopular among set theorists while simply negating CH doesn’t say much. In this talk, I will introduce Martin’s axiom as one way to govern extra reals obtained after negating CH, its extension Martin’s maximum, which actually fixes the size of the continuum to exactly א‎_2, and their connection to forcing and large cardinals. I will start with a friendly introduction to independence of CH and relative consistency. No previous knowledge other than basic facts about cardinality of the reals (not Julian’s standards) is required for this talk.