1,355 research outputs found
Some Ramsey theorems for finite -colorable and -chromatic graphs
Given a fixed integer , we prove Ramsey-type theorems for the classes of
all finite ordered -colorable graphs, finite -colorable graphs, finite
ordered -chromatic graphs, and finite -chromatic graphs.Comment: 7 page
Ramsey properties of products and pullbacks of categories and the Grothendieck construction
In this paper we provide purely categorical proofs of two important results
of structural Ramsey theory: the result of M.\ Soki\'c that the free product of
Ramsey classes is a Ramsey class and the result of M.\ Bodirsky that adding
constants to the language of a Ramsey class preserves the Ramsey property. The
proofs that we present here ignore the model-theoretic background of these
statements. Instead, they focus on categorical constructions by which the
classes can be constructed, generalizing the original statements along the way.
It turns out that the restriction to classes of relational structures, although
fundamental for the original proof strategies, is not relevant for the
statements themselves. The categorical proofs we present here remove all the
restrictions on the signature of first-order structures and provide the
information not only about the Ramsey property but also about the Ramsey
degrees
Ramsey precompact expansions of homogeneous directed graphs
In 2005, Kechris, Pestov and Todorcevic provided a powerful tool to compute
an invariant of topological groups known as the universal minimal flow,
immediately leading to an explicit representation of this invariant in many
concrete cases. More recently, the framework was generalized allowing for
further applications, and the purpose of this paper is to apply these new
methods in the context of homogeneous directed graphs.
In this paper, we show that the age of any homogeneous directed graph allows
a Ramsey precompact expansion. Moreover, we verify the relative expansion
properties and consequently describe the respective universal minimal flows
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
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