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AMENABILITY AND RAMSEY THEORY
RAMSEY THEORY
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2015/8/17
The purpose of this article is to connect the notion of the amenability of a discrete group with a new form of structural Ramsey theory. The Ramsey theoretic reformulation of amenability constitutes a...
Remarks for the Ramsey theory for trees
Remarks the Ramsey theory trees Combinatorics
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2011/9/21
Abstract: Extending Furstenberg's ergodic theoretic proof for Szemer\'edi's theorem on arithmetic progressions, Furstenberg and Weiss (2003) proved the following qualitative result. For every d and k,...
Transitive Sets in Euclidean Ramsey Theory
Transitive Euclidean Ramsey Theory
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2011/1/19
A finite set X in some Euclidean space Rn is called Ramsey if for any k there is a d such that whenever Rd is k-coloured it contains a monochromatic set congruent to X. This notion was introduced by E...
Ramsey Theory for Words Representing Rationals
Ramsey Theory Words Representing Rationals
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2010/11/9
Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for words over an infin...
Rothberger bounded groups and Ramsey theory
Rothberger bounded groups Ramsey theory
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2010/11/15
We show that: 1. Rothberger bounded subgroups of sigma-compact groups are characterized by Ramseyan partition relations. 2. For each uncountable cardinal $\kappa$ there is a ${\sf T}_0$ topological gr...