16 citations · 60 across the 30 of their papers we have counts for
5 papers · 1 filter
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…