Christina Brech

Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo (Brazil)

Set theory

Generalizing uniform families to the uncountable setting

Products of the Schreier family have been used in Banach space theory to built important objects such as the Tsirelson space. In order to generalize these constructions to the nonseparable setting, the families had to be generalized to uncountable index sets. We will present the link between the families and their corresponding Banach spaces and will focus on how to define and construct those families. More precisely, we will present the method (appearing in our recent joint work with Jordi Lopez-Abad and Stevo Todorcevic) to construct such families below the first Mahlo cardinal, which involves defining a family on a tree out of a family on its chains and a family on its antichains, and analyzing the combinatorial structure of it using Ramsey methods.


Christina Brech is an Assistant Professor at the University of São Paulo (Brazil) since 2010. Her research interests concentrate in applications of set theory to the geometry of Banach spaces, field on which she obtained her PhD degree in 2008, in a joint program (cotutelle) at the University of Paris 7 and at the University of São Paulo, under the codirection of Piotr Koszmider and Stevo Todorcevic.

She spent 18 months at the State University of Campinas (Brazil) as a postdoc in 2008-2009 and holds a research grant from CNPq (Bolsa de Produtividade em Pesquisa) since 2013. She is currently a member of the Committe on Logic in Latin America of the ASL and an ambassador of the Committee for Women in Mathematics of the IMU.