16 citations · 60 across the 30 of their papers we have counts for
40 papers
On the Consistency Strength of MM()
Natasha Dobrinen, John Krueger, Pedro Marun +2
We prove that the consistency strength of Martin's Maximum restricted to partial orders of cardinality follows from the consistency of ZFC.
Cofinal types of ultrafilters over measurable cardinals
Tom Benhamou, Natasha Dobrinen
We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the coun…
Characterisation of the big Ramsey degrees of the generic partial order
Martin Balko, David Chodounský, Natasha Dobrinen +4
As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite p…
Infinite-dimensional Ramsey theory for binary free amalgamation classes
Natasha Dobrinen, Andy Zucker
We develop infinite-dimensional Ramsey theory for Fraïssé limits of finitely constrained free amalgamation classes in finite binary languages. We show that our approach is optimal…
The Halpern--Läuchli Theorem at singular cardinals and failures of weak versions
Natasha Dobrinen, Saharon Shelah
This paper continues a line of investigation of the Halpern--Läuchli Theorem at uncountable cardinals. We prove in ZFC that the Halpern--Läuchli Theorem for one tree of height …
Fraisse structures with SDAP+, Part II: Simply characterized big Ramsey structures
Rebecca Coulson, Natasha Dobrinen, Rehana Patel
This is Part II of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. In…
Fraisse Structures with SDAP+, Part I: Indivisibility
Rebecca Coulson, Natasha Dobrinen, Rehana Patel
This is Part I of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. We p…
Infinite-dimensional Ramsey theory for homogeneous structures with SDAP
Natasha Dobrinen
We prove that for any homogeneous structure in a language with finitely many relation symbols of arity at most two satisfying SDAP (or LSDAP), there are spaces…
Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
Martin Balko, David Chodounský, Natasha Dobrinen +4
We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recen…
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.…
Big Ramsey degrees in universal inverse limit structures
Natasha Dobrinen, Kaiyun Wang
We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures,extending Zheng's work for the profinite graph to the setting of Fra\"…
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 …
Classes of barren extensions
Natasha Dobrinen, Daniel Hathaway
Henle, Mathias, and Woodin proved that, provided that holds in a model of ZF, then forcing with over adds no new sets of ordinals,…
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…
Borel sets of Rado graphs and Ramsey's Theorem
Natasha Dobrinen
The well-known Galvin-Prikry Theorem states that Borel subsets of the Baire space are Ramsey: Given any Borel subset , where is endowed with the…
The Ramsey Theory of Henson graphs
Natasha Dobrinen
Analogues of Ramsey's Theorem for infinite structures such as the rationals or the Rado graph have been known for some time. In this context, one looks for optimal bounds, called d…
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…
Banach Spaces from Barriers in High Dimensional Ellentuck Spaces
Alvaro Arias, Natasha Dobrinen, Gabriel Giron-Garnica +1
A new hierarchy of Banach spaces , any positive integer, is constructed using barriers in high dimensional Ellentuck spaces \cite{DobrinenJSL15} following the classic…
Perfect Tree Forcings for Singular Cardinals
Natasha Dobrinen, Dan Hathaway, Karel Prikry
We investigate forcing properties of perfect tree forcings defined by Prikry to answer a question of Solovay in the late 1960's regarding first failures of distributivity. Given a…
Forcing and the Halpern-Läuchli Theorem
Natasha Dobrinen, Dan Hathaway
We investigate the effects of various forcings on several forms of the Halpern-Läuchli Theorem. For inaccessible , we show they are preserved by forcings of size less than .…
Forcing in Ramsey theory
Natasha Dobrinen
Ramsey theory and forcing have a symbiotic relationship. At the RIMS Symposium on Infinite Combinatorics and Forcing Theory in 2016, the author gave three tutorials on Ramsey theor…
The Ramsey theory of the universal homogeneous triangle-free graph
Natasha Dobrinen
The universal homogeneous triangle-free graph, constructed by Henson and denoted , is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Ra…