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Local Ramsey Theory in abstract spaces

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Mathematical, Foundational and Computational Aspects of the Higher Infinite

We study the notion of semiselectiviy for coideals of the space of infinite sets of natural numbers, and propose a generalization to abstract Ramsey spaces. We also consider the corresponding forcing notions. Abstract Ramsey spaces in the sense of Todorcevic [1] provide a general framework that unifies several Ramsey type results.

[1] Todorcevic, S. Introduction to Ramsey spaces. Princeton University Press, 2010.

This talk is part of the Isaac Newton Institute Seminar Series series.

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