16 citations · 60 across the 30 of their papers we have counts for
5 papers · 1 filter
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…
Topological Ramsey Spaces Dense in Forcings
Natasha Dobrinen
Topological Ramsey spaces are spaces which support infinite dimensional Ramsey theory similarly to the Ellentuck space. Each topological Ramsey space is endowed with a partial orde…