2 citations · 2 across the 3 of their papers we have counts for
7 papers
Ramsey theory of homogeneous structures: current trends and open problems
Natasha Dobrinen
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems.…
Fraisse classes with simply characterized big Ramsey degrees
Rebecca Coulson, Natasha Dobrinen, Rehana Patel
We formulate a property strengthening the Disjoint Amalgamation Property and prove that every Fraisse structure in a finite relational language with relation symbols of arity at mo…
The Ramsey theory of the universal homogeneous triangle-free graph Part II: Exact big Ramsey degrees
Natasha Dobrinen
Building on previous work of the author, for each finite triangle-free graph , we determine the equivalence relation on the copies of inside the universal…
Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces
Natasha Dobrinen, Sonia Navarro Flores
This paper investigates properties of -closed forcings which generate ultrafilters satisfying weak partition relations. The Ramsey degree of an ultrafilter for …
Ramsey Theory on Infinite Structures and the Method of Strong Coding Trees
Natasha Dobrinen
This article discusses some recent trends in Ramsey theory on infinite structures. Trees and their Ramsey theory have been vital to these investigations. The main ideas behind the…
A List of Problems on the Reverse Mathematics of Ramsey Theory on the Rado Graph and on Infinite, Finitely Branching Trees
Natasha Dobrinen
This list presents problems in the Reverse Mathematics of infinitary Ramsey theory which I find interesting but do not personally have the techniques to solve. The intent is to enl…