Mar
08
Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.
Friday, March 16 , 2018
2:30 p.m.
Fields Institute – 210
PhD Candidate: Fulgencio Lopez
Supervisor: Stevo Todorcevic
Thesis title: Construction schemes and their applications
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We study capturing construction schemes, a new combinatorial tool introduced by Todorcevíc to build uncountable structures. It consists of a ranked family of finite sets that provides a framework to do recursive constructions of uncountable objects by working with finite amal-gamations of finite isomorphic substructures, the uncountable substructures of the final object can be further study using capturing.
In this Thesis we study the consistency of capturing construction schemes, and related defi-
nitions, we prove results of consistency, and give several applications of this tool both to infinite combinatorics and Banach space theory. For example, we show weaker forms of capturing, such as n-capturing, form a strict hierarchy which is related to the m-Knaster Hierarchy. We also show how capturing construction schemes can be used in constructing Suslin trees and Haus-dorff gaps of a special kind in an intuitive manner. And give some applications to the theory of nonseparable Banach spaces.
A copy of the thesis: Thesis Fulgencio Lopez
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