Natasha Dobrinen
Published 2019-09-12Version 1
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 author's recent method of trees with coding nodes are presented, showing how they can be useful both for coding structures with forbidden configurations as well as those with none. Using forcing as a tool for finite searches has allowed the development of Ramsey theory on such trees, leading to solutions for finite big Ramsey degrees of Henson graphs as well as infinite dimensional Ramsey theory of copies of the Rado graph. Possible future directions for applications of these methods are discussed.
Comments: 24 pages, Invited submission for the upcoming Research Trends in Contemporary Logic
The universal triangle-free graph has finite big Ramsey degrees
Fraïssé's Conjecture and big Ramsey degrees of structures admitting finite monomorphic decomposition
A note on big Ramsey degrees
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