ﻻ يوجد ملخص باللغة العربية
We define a collection of topological Ramsey spaces consisting of equivalence relations on $omega$ with the property that the minimal representatives of the equivalence classes alternate according to a fixed partition of $omega$. To prove the associated pigeonhole principles, we make use of the left-variable Hales-Jewett theorem and its extension to an infinite alphabet. We also show how to transfer the corresponding infinite-dimensional Ramsey results to equivalence relations on countable limit ordinals (up to a necessary restriction on the set of minimal representatives of the equivalence classes) in order to obtain a dual Ramsey theorem for such ordinals.
We study the topological version of the partition calculus in the setting of countable ordinals. Let $alpha$ and $beta$ be ordinals and let $k$ be a positive integer. We write $betato_{top}(alpha,k)^2$ to mean that, for every red-blue coloring of the
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces - called ultrahomogeneous - is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present p
This paper investigates properties of $sigma$-closed forcings which generate ultrafilters satisfying weak partition relations. The Ramsey degree of an ultrafilter $mathcal{U}$ for $n$-tuples, denoted $t(mathcal{U},n)$, is the smallest number $t$ such
We investigate interactions between Ramsey theory, topological dynamics, and model theory. We introduce various Ramsey-like properties for first order theories and characterize them in terms of the appropriate dynamical properties of the theories in
Inspired by Ramseys theorem for pairs, Rival and Sands proved what we refer to as an inside/outside Ramsey theorem: every infinite graph $G$ contains an infinite subset $H$ such that every vertex of $G$ is adjacent to precisely none, one, or infinite