Breadcrumb
Iterated Forcing with Side Conditions
Mon 25 February 2013, 17:00
David Aspero
University of East Anglia, Norwich
Organisers: Philip Welch, Peter Holy
ABSTRACT
I will present a method for building forcing iterations with symmetric matrices of countable structures as side conditions in order to ensure properness. The iterations will be arbitrarily long and will have the
$\aleph_2$--chain condition. The idea of using this type of matrices as
side conditions to ensure properness in contexts where one wants to obtain a forcing with the $\aleph_2$--c.c.\ is natural and not new. The novelty here is that the side conditions now affect whole iterations (or initial segments thereof). As an application I will show the consistency of a generalization of Martin's Axiom to a natural class of forcing notions with the $\aleph_2$--chain condition. This is joint work with Miguel Angel Mota.