13 research outputs found
On Galvin's lemma and Ramsey spaces
An abstract version of Galvin's lemma is proven, within the framework of the
theory of Ramsey spaces. Some instances of it are explored.Comment: Accepted in Annals of Combinatoric
Big Ramsey degrees using parameter spaces
We show that the universal homogeneous partial order has finite big Ramsey
degrees and discuss several corollaries. Our proof uses parameter spaces and
the Carlson-Simpson theorem rather than (a strengthening of) the
Halpern-L\"auchli theorem and the Milliken tree theorem, which are the primary
tools used to give bounds on big Ramsey degrees elsewhere (originating from
work of Laver and Milliken).
This new technique has many additional applications. To demonstrate this, we
show that the homogeneous universal triangle-free graph has finite big Ramsey
degrees, thus giving a short proof of a recent result of Dobrinen.Comment: 19 pages, 2 figure
Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups
We study in this paper some connections between the Fraisse theory of
amalgamation classes and ultrahomogeneous structures, Ramsey theory, and
topological dynamics of automorphism groups of countable structures.Comment: 73 pages, LaTeX 2e, to appear in Geom. Funct. Ana
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory
The goal of this present manuscript is to introduce the reader to the
nonstandard method and to provide an overview of its most prominent
applications in Ramsey theory and combinatorial number theory.Comment: 126 pages. Comments welcom