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The Ramsey Theory of Ordinals

Speaker: Thilo Weinert, Ben-Gurion University of the Negev

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Abstract: Ramsey Theory is a branch of mathematics that is oftentimes summed up by the slogan “complete disorder is impossible”. A classical example is a Theorem on Friends and Strangers stating that in every party with six guests there is a group of three people who are either all mutually acquainted or all mutually unacquainted. More abstractly this amounts to asking whether for an edge-coloring of a complete graph there is a homogeneous set of vertices (a set of vertices such that all edges between them get the same color) of a certain size. This problem can be considered both in the finite and infinite. In the infinite, considering structural aspects as simple as the order can make a difference. We are going to consider these questions for the simplest cases of infinite linearly ordered sets—countable ordinals.

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