Automorphisms of $\mathcal{P}(\lambda)/I_{\kappa}$, for $\lambda$ uncountable | Department of Mathematics

Automorphisms of $\mathcal{P}(\lambda)/I_{\kappa}$, for $\lambda$ uncountable

Event Information
Event Location: 
GAB 461 (Refreshments in GAB 472 at 3:30pm)
Event Date: 
Monday, April 20, 2015 - 4:00pm

We will discuss automorphisms of $\mathcal{P}(\lambda)/I_{\kappa}$, for $\kappa \leq \lambda$ infinite cardinals, where $I_{\kappa}$ denotes the ideal of sets of cardinality less than $\kappa$. After surveying what we know about the state of the subject, we will present an argument which shows (among other things) that Martin's Axiom implies that every automorphism of $\mathcal{P}(2^{\aleph_{0}})/Fin$ is trivial off of a countable set. By recent results of Shelah and Steprans, $2^{\aleph_{0}}$ can be replaced here with any cardinal below the least strongly inaccessible.