# Miguel Angel Mota: On a question of Abraham and Cummings

15/March/2013, 13:30–15:00
Fields institute,Room 210

Speaker: Miguel Angel Mota

Title: On a question of Abraham and Cummings

Abstract: The technique of ensuring properness of a given forcing notion by incorporating elementary substructures of some large enough model into its definition as side conditions may be traced back to Todorcevic. The more specific approach of considering symmetric systems of countable structures as side conditions in the context in which one starts with a model of CH and wants to obtain a forcing notion which is proper and does not collapse cardinals is quite natural. In fact, this approach (also created by Todorcevic) has already shown up in several places in the literature. The main novelty of the method created by Asperó and Mota is that it incorporates the use of symmetric systems of structures as side conditions affecting all iterands of a given forcing iteration rather than a single forcing as in the above references. As an interesting application of this method, we answer a question of Abraham and Cummings by showing that a negative polychromatic Ramsey relation is consistent together with MA and a large continuum. This is joint work with Asperó