14/05/2022
Dear all, the AUC Mathematics Department cordially invites you to attend the MACT Senior Thesis presentation of Abdelrahman Ibrahim this Thursday, 19.05.2022, 6:30pm.
Title: Fraissé Structures and Stationary Independence Relations
Abstract: Model theory allows us to abstract notions from pure mathematics to study them from the point of view of first order logic. Most prominent among these is the notion of independence. In this talk, we focus on a specific independence relation, called stationary independence. Under certain conditions on the structure, the presence of a stationary independence allows strong conclusions about its automorphism group G, like the study of its normal subgroup structure. In so-called homogenous structures, or Fraissé structures, with stationary independence, the automorphism group turns out to be universal, i.e., every automorphism group of a substructure can be viewed as a closed subgroup of G itself.
In a conference in Istanbul in 2014, it was asked whether one can define a stationary independence relation on the rationals as a linear order, which turns out to be false. Generalizing this, we provide a novel necessary condition for the existence of a stationary independence relation.
In this talk, we give a gentle introduction to Model theory and Fraïssé structures, and then move on to work with stationary independence relations, reaching up to our novel condition.
