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Introduction to Ramsey Spaces
Partitioning pairs of countable ordinals
On montre que les paires d'ordinaux denombrables peuvent etre colorees avec une infinite non denombrable de couleurs de telle sorte que tout ensemble non denombrable contienne des paires de chaqueExpand
We study in this paper graph coloring problems in the context of descriptive set theory. We consider graphs G=(X, R), where the vertex set X is a standard Borel space (i.e., a complete separableExpand
Trees and Linearly Ordered Sets
Publisher Summary This chapter presents an introduction to several problems concerning trees and linearly ordered sets and the dualities between them. Several classes of trees and linearly orderedExpand
Walks On Ordinals And Their Characteristics
Walks on Countable Ordinals.- Metric Theory of Countable Ordinals.- Coherent Mappings and Trees.- The Square-bracket Operation on Countable Ordinals.- General Walks and Their Characteristics.- SquareExpand
Directed sets and cofinal types
We show that 1, S. @1, X x xl and [l]<@ are the only cofinal types of directed sets of size Sl, but that there exist many cofinal types of directed sets of size continuum. A partially ordered set DExpand